ࡱ>  t3bjbj_W_W .====t*ppppp,U4       ,M-p     dpp  ddd Rp p d ddd8^c^d%0Uddddpd<   d   U          6:   Graphical Method of Solution of a Linear Programming Problem  INCLUDEPICTURE "http://www.tutorvista.com/images/trans_pix.gif" \* MERGEFORMATINET So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x1, x2, x3, ..... xn, which can optimize (maximize or minimize) the objective function Z, then we say that these values of xi are the optimal solution of the Linear Program (LP).The graphical method is applicable to solve the LPP involving two decision variables x1, and x2, we usually take these decision variables as x, y instead of x1, x2. To solve an LP, the graphical method includes two major steps. a) The determination of the solution space that defines the feasible solution. Note that the set of values of the variable x1, x2, x3,....xn which satisfy all the constraints and also the non-negative conditions is called the feasible solution of the LP.b) The determination of the optimal solution from the feasible region. a) To determine the feasible solution of an LP, we have the following steps. Step 1: Since the two decision variable x and y are non-negative, consider only the first quadrant of xy-coordinate plane  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img47.gif" \* MERGEFORMATINET Draw the line ax + by = c (1)For each constraint,the line (1) divides the first quadrant in to two regions say R1 and R2, suppose (x1, 0) is a point in R1. If this point satisfies the in equation ax + by c or ( c), then shade the region R1. If (x1, 0) does not satisfy the inequality, shade the region R2.Step 3: Corresponding to each constant, we obtain a shaded region. The intersection of all these shaded regions is the feasible region or feasible solution of the LP. Let us find the feasible solution for the problem of a decorative item dealer whose LPP is to maximize profit function. Z = 50x + 18y (1)Subject to the constraints INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img49.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img50.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img51.gif" \* MERGEFORMATINET Step 1: Since x INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img52.gif" \* MERGEFORMATINET 0, y INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img53.gif" \* MERGEFORMATINET 0, we consider only the first quadrant of the xy - plane Step 2: We draw straight lines for the equation 2x+ y = 100 (2)x + y = 80 To determine two points on the straight line 2x + y = 100 Put y = 0, 2x = 100  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img54.gif" \* MERGEFORMATINET x = 50  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img55.gif" \* MERGEFORMATINET (50, 0) is a point on the line (2)put x = 0 in (2), y =100 INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img56.gif" \* MERGEFORMATINET (0, 100) is the other point on the line (2)Plotting these two points on the graph paper draw the line which represent the line 2x + y =100.  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img57.gif" \* MERGEFORMATINET This line divides the 1st quadrant into two regions, say R1 and R2. Choose a point say (1, 0) in R1. (1, 0) satisfy the inequality 2x + y  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img58.gif" \* MERGEFORMATINET 100. Therefore R1 is the required region for the constraint 2x + y  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img59.gif" \* MERGEFORMATINET 100.Similarly draw the straight line x + y = 80 by joining the point (0, 80) and (80, 0). Find the required region say R1', for the constraint x + y  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img60.gif" \* MERGEFORMATINET 80. The intersection of both the region R1 and R1' is the feasible solution of the LPP. Therefore every point in the shaded region OABC is a feasible solution of the LPP, since this point satisfies all the constraints including the non-negative constraints.b) There are two techniques to find the optimal solution of an LPP.Corner Point MethodThe optimal solution to a LPP, if it exists, occurs at the corners of the feasible region.The method includes the following steps Step 1: Find the feasible region of the LLP. Step 2: Find the co-ordinates of each vertex of the feasible region.These co-ordinates can be obtained from the graph or by solving the equation of the lines. Step 3: At each vertex (corner point) compute the value of the objective function.Step 4: Identify the corner point at which the value of the objective function is maximum (or minimum depending on the LP)The co-ordinates of this vertex is the optimal solution and the value of Z is the optimal value Example: Find the optimal solution in the above problem of decorative item dealer whose objective function is Z = 50x + 18y.In the graph, the corners of the feasible region are O (0, 0), A (0, 80), B(20, 60), C(50, 0) At (0, 0) Z = 0 At (0, 80) Z = 50 (0) + 18(80)= 1440At (20, 60), Z = 50 (20) +18 (60)= 1000 + 1080 = Rs.2080At (50, 0) Z = 50 (50 )+ 18 (0)= 2500.Since our object is to maximize Z and Z has maximum at (50, 0) the optimal solution is x = 50 and y = 0.The optimal value is 2500.If an LPP has many constraints, then it may be long and tedious to find all the corners of the feasible region. There is another alternate and more general method to find the optimal solution of an LP, known as 'ISO profit or ISO cost method'ISO- PROFIT (OR ISO-COST)Method of Solving Linear Programming ProblemsSuppose the LPP is to Optimize Z = ax + by subject to the constraints INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img61.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img62.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img63.gif" \* MERGEFORMATINET This method of optimization involves the following method.Step 1: Draw the half planes of all the constraintsStep 2: Shade the intersection of all the half planes which is the feasible region.Step 3: Since the objective function is Z = ax + by, draw a dotted line for the equation ax + by = k, where k is any constant. Sometimes it is convenient to take k as the LCM of a and b. Step 4: To maximise Z draw a line parallel to ax + by = k and farthest from the origin. This line should contain at least one point of the feasible region. Find the coordinates of this point by solving the equations of the lines on which it lies.To minimise Z draw a line parallel to ax + by = k and nearest to the origin. This line should contain at least one point of the feasible region. Find the co-ordinates of this point by solving the equation of the line on which it lies. Step 5: If (x1, y1) is the point found in step 4, then x = x1, y = y1, is the optimal solution of the LPP and Z = ax1 + by1 is the optimal value. The above method of solving an LPP is more clear with the following example.Example: Solve the following LPP graphically using ISO- profit method.maximize Z =100 + 100y. Subject to the constraints  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img64.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img65.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img66.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img67.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img68.gif" \* MERGEFORMATINET Suggested answer:since x INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img69.gif" \* MERGEFORMATINET 0, y INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img70.gif" \* MERGEFORMATINET 0, consider only the first quadrant of the plane graph the following straight lines on a graph paper 10x + 5y = 80 or 2x+y =166x + 6y = 66 or x +y =11 4x+ 8y = 24 or x+ 2y = 6 5x + 6y = 90Identify all the half planes of the constraints. The intersection of all these half planes is the feasible region as shown in the figure.  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img71.gif" \* MERGEFORMATINET Give a constant value 600 to Z in the objective function, then we have an equation of the line 120x + 100y = 600 (1)or 6x + 5y = 30 (Dividing both sides by 20)P1Q1 is the line corresponding to the equation 6x + 5y = 30. We give a constant 1200 to Z then the P2Q2 represents the line.120x + 100y = 1200 6x + 5y = 60P2Q2 is a line parallel to P1Q1 and has one point 'M' which belongs to feasible region and farthest from the origin. If we take any line P3Q3 parallel to P2Q2 away from the origin, it does not touch any point of the feasible region. The co-ordinates of the point M can be obtained by solving the equation 2x + y = 16 x + y =11 which give x = 5 and y = 6  INCLUDEPICTURE "http://content.tutorvista.com/maths/content/us/class12maths/chapter08/images/img72.gif" \* MERGEFORMATINET The optimal solution for the objective function is x = 5 and y = 6The optimal value of Z 120 (5) + 100 (6) = 600 + 600 = 1200 >?@, - 0 1 4 5 > ? R 7 8 ? ƳƛƳ޳scScS޳޳hJB*OJQJ^JaJphhDB*OJQJ^JaJph%hDhlB*OJQJ^JaJph(hDh*B*H*OJQJ^JaJph.jUhDh*B*OJQJU^JaJph%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJ+hDh*5B*OJQJ\^JaJph >? fNkd$$Ift"x  634ap yt|>kd$$Ift"x634ayt| dP$Ifgd* u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdg$$Ift"x634ayt|? @    G H K L O P V W Y     ( G g h j k r g h ؽؽؽؽؽؽؽؽؽؽ؏.jhDh*B*OJQJU^JaJph+hDh*5B*OJQJ\^JaJphh*h*CJaJhJB*OJQJ^JaJph%hDh*B*OJQJ^JaJph(hDh*B*H*OJQJ^JaJph/  u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdf$$Ift"x634ayt|    g h j u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kde$$Ift"x634ayt|j k k u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdd$$Ift"x634ayt|h i j k l m n ^bln*,dftvнzzee(hDh*B*H*OJQJ^JaJph%hDh*B*OJQJ^JaJph(hDh*B*H*OJQJ^JaJphhJB*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.jchDh*B*OJQJU^JaJph'k l m n u6>kd $$Ift"x634ayt|>kdF $$Ift"x634ayt| dP$Ifgd*>kd $$Ift"x634ayt| u6>kd$$Ift"x634ayt|>kdE$$Ift"x634ayt| dP$Ifgd*>kd $$Ift"x634ayt|u6>kd$$Ift"x634ayt|>kdD$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|  "#/012346789:ֻֻֻֻֻֻֻֻֻֻ֣֣sֻֻ֣.jhDh*B*OJQJU^JaJph.jAhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJhJB*OJQJ^JaJph%hDh*B*OJQJ^JaJph+hDh*5B*OJQJ\^JaJph+ "#u6>kd$$Ift"x634ayt|>kdC$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|u6>kd$$Ift"x634ayt|>kdB$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|3467u6>kd$$Ift"x634ayt|>kdJ$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|=>?u6>kd"$$Ift"x634ayt|>kd6$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|:;<=>?@GOPPQRS15678DEннЄннlн\hJB*OJQJ^JaJph.j'hDh*B*OJQJU^JaJph.j+#hDh*B*OJQJU^JaJph+hDh*5B*OJQJ\^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph$?@u6>kdn,$$Ift"x634ayt|>kd,$$Ift"x634ayt| dP$Ifgd*>kd"$$Ift"x634ayt|567u6>kdm-$$Ift"x634ayt|>kd-$$Ift"x634ayt| dP$Ifgd*>kd,$$Ift"x634ayt|78DEGHu6>kdl.$$Ift"x634ayt|>kd.$$Ift"x634ayt| dP$Ifgd*>kd-$$Ift"x634ayt|EGH ()+,-mnopɱəɁ.j;hDh*B*OJQJU^JaJph.j65hDh*B*OJQJU^JaJph.j0hDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph0u6>kdk/$$Ift"x634ayt|>kd/$$Ift"x634ayt| dP$Ifgd*>kd.$$Ift"x634ayt|()+,u6>kd4$$Ift"x634ayt|>kd4$$Ift"x634ayt| dP$Ifgd*>kd/$$Ift"x634ayt|u6>kdW:$$Ift"x634ayt|>kd:$$Ift"x634ayt| dP$Ifgd*>kd9$$Ift"x634ayt|u6>kd?$$Ift"x634ayt|>kdx?$$Ift"x634ayt| dP$Ifgd*>kd:$$Ift"x634ayt|u6>kd|Y$$Ift"x634ayt|>kdw@$$Ift"x634ayt| dP$Ifgd*>kd"@$$Ift"x634ayt| STнxн`нн.j&ZhDh*B*OJQJU^JaJphhJB*OJQJ^JaJph(hDh*B*H*OJQJ^JaJph(hDh*B*H*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.j@hDh*B*OJQJU^JaJph[\]^tu6>kdic$$Ift"x634ayt|>kdc$$Ift"x634ayt| dP$Ifgd*>kdY$$Ift"x634ayt|TUV[\]^lmnotuvwuvxy3467`acdннЅнo+hDh*5B*OJQJ\^JaJphf.jchDh*B*OJQJU^JaJph(hDh*B*H*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.j^hDh*B*OJQJU^JaJph*tuvwuvxu6>kdh$$Ift"x634ayt|>kdh$$Ift"x634ayt| dP$Ifgd*>kd5h$$Ift"x634ayt|xyu6>kdi$$Ift"x634ayt|>kdi$$Ift"x634ayt| dP$Ifgd*>kd4i$$Ift"x634ayt|346u6>kdj$$Ift"x634ayt|>kdj$$Ift"x634ayt| dP$Ifgd*>kd3j$$Ift"x634ayt|67`acdu6>kdk$$Ift"x634ayt|>kdk$$Ift"x634ayt| dP$Ifgd*>kd2k$$Ift"x634ayt|dk:;<=D stvw. / 1 2 \ ] _ ` q r s t !!!! !!!!!3!ֻ˻˻˻hJB*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph+hDh*5B*OJQJ\^JaJphJu6>kdl$$Ift"x634ayt|>kdl$$Ift"x634ayt| dP$Ifgd*>kd1l$$Ift"x634ayt|:;<=u6>kdm$$Ift"x634ayt|>kdm$$Ift"x634ayt| dP$Ifgd*>kd0m$$Ift"x634ayt|u6>kdn$$Ift"x634ayt|>kdn$$Ift"x634ayt| dP$Ifgd*>kd/n$$Ift"x634ayt|stvwu6>kdo$$Ift"x634ayt|>kdo$$Ift"x634ayt| dP$Ifgd*>kd.o$$Ift"x634ayt|. / 1 u6>kdp$$Ift"x634ayt|>kdp$$Ift"x634ayt| dP$Ifgd*>kd-p$$Ift"x634ayt|1 2 \ ] _ ` q u6>kdq$$Ift"x634ayt|>kdq$$Ift"x634ayt| dP$Ifgd*>kd,q$$Ift"x634ayt|q r s t u6>kdr$$Ift"x634ayt|>kdr$$Ift"x634ayt| dP$Ifgd*>kd+r$$Ift"x634ayt| u6>kds$$Ift"x634ayt|>kds$$Ift"x634ayt| dP$Ifgd*>kd*s$$Ift"x634ayt| u6>kdt$$Ift"x634ayt|>kd~t$$Ift"x634ayt| dP$Ifgd*>kd)t$$Ift"x634ayt| !!!!!u6>kdu$$Ift"x634ayt|>kd}u$$Ift"x634ayt| dP$Ifgd*>kd(u$$Ift"x634ayt|!!!!~!!!u6>kdv$$Ift"x634ayt|>kd|v$$Ift"x634ayt| dP$Ifgd*>kd'v$$Ift"x634ayt|3!~!!!!!!!!!J"i""""""""""""""""##2#3#5#6#7##########8$9$u.jw{hDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph+hDh*5B*OJQJ\^JaJph+hDh*5B*OJQJ\^JaJphfhJB*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph,!!!!!!"u6>kdw$$Ift"x634ayt|>kd{w$$Ift"x634ayt| dP$Ifgd*>kd&w$$Ift"x634ayt|"""""""u6>kdx$$Ift"x634ayt|>kdzx$$Ift"x634ayt| dP$Ifgd*>kd%x$$Ift"x634ayt|"""""""u6>kdy$$Ift"x634ayt|>kdyy$$Ift"x634ayt| dP$Ifgd*>kd$y$$Ift"x634ayt|""##2#3#5#u6>kdz$$Ift"x634ayt|>kdxz$$Ift"x634ayt| dP$Ifgd*>kd#z$$Ift"x634ayt|5#6#####<$u6>kdQ$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd"{$$Ift"x634ayt|9$:$;$<$=$?$@$A$$$$$$$$$$%%% %7%8%:%;%B%%%%%%O&P&R&S&Z&J'K'M'N':(;(=(>(E(K(ннКн+hDh*5B*OJQJ\^JaJph.jԇhDh*B*OJQJU^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph-<$=$?$@$$$$u6>kd،$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd*$$Ift"x634ayt|$$$%%%7%u6>kd׍$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd-$$Ift"x634ayt|7%8%:%;%%%%u6>kd֎$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd,$$Ift"x634ayt|%%O&P&R&S&J'u6>kdՏ$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd+$$Ift"x634ayt|J'K'M'N':(;(=(u6>kdԐ$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd*$$Ift"x634ayt|=(>(v(w(y(z((u6>kdӑ$$Ift"x634ayt|>kd~$$Ift"x634ayt| dP$Ifgd*>kd)$$Ift"x634ayt|K(L(O(P(v(w(y(z(((((((((((((((((((,)-)/)0)8)w)x)z){))))))))))5*6*7*8*9*:*<*=*>**طͷ͟؟͟.j$hDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph+hDh*5B*OJQJ\^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph(hDh*B*H*OJQJ^JaJph5(((((((u6>kdҒ$$Ift"x634ayt|>kd}$$Ift"x634ayt| dP$Ifgd*>kd($$Ift"x634ayt|((,)-)/)0)w)u6>kdѓ$$Ift"x634ayt|>kd|$$Ift"x634ayt| dP$Ifgd*>kd'$$Ift"x634ayt|w)x)z){))))u6>kdД$$Ift"x634ayt|>kd{$$Ift"x634ayt| dP$Ifgd*>kd&$$Ift"x634ayt|))))))9*u6>kdϕ$$Ift"x634ayt|>kdz$$Ift"x634ayt| dP$Ifgd*>kd%$$Ift"x634ayt|9*:*<*=****u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd6$$Ift"x634ayt|*********?+@+A+B+C+D+F+G+H++++++++++I,J,K,L,M,N,P,Q,轲轲轲j轲.jhDh*B*OJQJU^JaJph.j\hDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph"**C+D+F+G++u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdO$$Ift"x634ayt|++++M,N,P,u6>kd $$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdk$$Ift"x634ayt|P,Q,c,d,f,g,-u6>kd $$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd`$$Ift"x634ayt|Q,b,c,d,f,g,n,o,,,,,,,o-p-q-r--------- . .....1.2.4.5.B.C.E.F......R/ֳֳֳֳs˳hJB*OJQJ^JaJph.jַhDh*B*OJQJU^JaJph.j_hDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph+hDh*5B*OJQJ\^JaJph--------u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdM$$Ift"x634ayt|--....1.u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdL$$Ift"x634ayt|1.2.4.5.B.C.E.u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdK$$Ift"x634ayt|E.F.....V/u6>kd$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kdJ$$Ift"x634ayt|R/S/T/U/V/W/Y/Z////00000B0C0E0F0G0H0I0J00000000000000000000000 1 111z1{1|1}111轲(hDh*B*H*OJQJ^JaJphhJB*OJQJ^JaJphh*h*CJaJ%hDh*B*OJQJ^JaJph.jIhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJph7V/W/Y/Z///0u6>kd_$$Ift"x634ayt|>kd $$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|0000B0C0E0u6>kd^$$Ift"x634ayt|>kd $$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|E0F000000u6>kd]$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|0000000u6>kd\$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|00111132u6>kd[$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|111111132426272M2N2P2Q2b2c2d2e2f22222(3)3+3,3D3E3G3H3g3h3j3k3r3s3t3̴촜̘hu.jhDh*B*OJQJU^JaJph.jhDh*B*OJQJU^JaJphh*h*CJaJ(hDh*B*H*OJQJ^JaJph%hDh*B*OJQJ^JaJph&32426272M2N2P2u6>kdZ$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|P2Q2b2c2d2e2(3u6>kdY$$Ift"x634ayt|>kd$$Ift"x634ayt| dP$Ifgd*>kd$$Ift"x634ayt|(3)3+3,3D3E3G3u6>kd$$Ift"x634ayt|>kdz$$Ift"x634ayt| dP$Ifgd*>kd%$$Ift"x634ayt|G3H3g3h3j3k3r3u6>kd$$Ift"x634ayt|>kdy$$Ift"x634ayt| dP$Ifgd*>kd$$$Ift"x634ayt|r3s3t3>kd#$$Ift"x634ayt|,1h/ =!"#$% S$$If!vh#v":V 6,5x34 yt|Dd R  C .trans_pixr$$If!vh#v":V  6,5x34 p yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|DdhP  S ,A img47b'< :担n'< :担PNG  IHDRkPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsCIDAThCX[r Ir[6iWH643&5B] ^Gd`{D+!$X@/*zaFmCө,a)yxPC=]/X|ЉS&y{cM{Iyo.W\ P\5ؿeh¶[q{jnYeef!muO.3u(Jn&b̄@_1rFL z o|f`8t8g'Z!Ȭ'M@FePR[ ?|4Eԕc}&HV8a*=&멚JV:wD,(hWSR 1sHj.h Ohaj1 $; ˖A3 D.⌦G׹Dc.0. 讓#s[˞Zw0 NHi3ؑ=s@2Jj"#)Ġ,:O+L=iVO*phԖPEG*p0FUZLUtlhJRz @W{yhk#ݷI[wT4QH ]8k(*zv?ݣg-@w8}F,Y6iS{,5juh)y֝-uVo+_Z@%{M]Da!Qo/psw+w6HW TO!Q[ہw7&2aSg 虔s{U ݶb8[75.WK3b/E[?F,|YvIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt| Ddd;P  S ,A img49be/:Uv]An9/:Uv]PNG  IHDR\fyPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKՔA DMMp@-"WtpAv9ʊ#Fd}K2#,2/D/ Pp#&_odTCi_]B諎Đ,)aLu*Rm*a2M6Q(.Tns7Ut: b_tZ'.ie uIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dde;P  S ,A img50bI'eL %8n'eL PNG  IHDRK9_PLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDAT8OݔY D R?tE0)*%:@ (Waz7-0H$YLۘ8֗'i*p ٍ]^6/$$bjCp./|ш~@=@,)}F7׳cw;s#~wιUA IENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|DdU;P  S ,A img51bR*>5{])D.n&*>5{])DPNG  IHDR[bPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKK D#"llJ~&J7=t [RJXXd."E'J$BƠXB3Z鄒 h6D y"@b_GhAn$L1>_GhPNG  IHDR42CܰPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HseIDATx^I=3EGG5vxxKPKRK !:I@ ._V6䗿i~ {{>: ZV=9}0hA/A+ݓCЧ & 4|p4NdY޶5d1VkmY &{ꟘF[M΢}Ml!d,cb<+:@ӽ"G[F MZ|-&S%?s Tt)wRt IyB -,tL{DvGi^gXHh@Y=c6?mkRk o)=Жm44-"i=ЖR{-Cm=% )=+R{Am Z;mXjUhc=֡@[6+4Wj hk)YmhmpS\祈߳r^Q݆kqwB,AJ6z\-\.4{>Zm};vmrDqw֘S TuOQ􀼗ۗ껧z\U cݳenYR4iML "`= KjD@CBAiϵWN};8-YR3кlj|;fAk{;fĚ^j.4,OXz0 +9:=v"sk@ f@ f&Z4-Z4-Z4%Z4%Z4) Ml!$ 8cb C5c"M-IfAQZnepV6$(4qۨ\~b8l؀V( ohRj?M8TqY{V,G) ^률薐MMAFd44A䙣6$o䴂/9 Z.eУ^U4jh 1"~GJ{ӘFG%p [HOZc+*hyQR}z.ʏ*}T0fA84%6l !jVfOvg($Rl<b+YnsxMQ>KjL/{~Li'P>Ex`YQ5%4{NP3Д*S;%ǘZTR!X5iYi#j4{[``Kj]Yܺz{?/rv%5:ҒvH͊尥}RV Y,Ue'ݾszZR{&G,5%5ٲvS{j4!]Iņ660v70|հJ'6feZQ%󅦩9Fj,-74ÉfjBb%7>:恚emE@0,ܐggI ADHvBY<"@tA%iÄvhJ'/YG";@OeDv0* "@(ze!(R#1&3a*/)h2\C4eg[!*< (zk  ǰK- TA( )*@vݢu,9\j NfL],t]eU:ͥ 8)Sf`E3\jMBA=t&P m>@eYah ZCVu0Mo,$4ap,FiZ!Ĥ 0RKKjд%`h=Z%%`hɱ6B[$M0)tZKIj[ɉ6@ӋC-!ClZ:R/rMMGj,fݸ6!l%Bɢ NjCecpꅮ';. 9 w)^W?SP \2x2 ڈY+*HMzba`SP9K$Z fz[cVF)-ޟEdٺhTgLI' @`"'ܔdph35%5uXoNqɐ ݳ42U:j0YfU1 q 5FU? fh.5KqCJU.FŪUGWz$8FNl/ uWXcj(M_zSxc25uә=]~aK#aYF#0X2s2*KiG`M Eϻi }97Xgm 'V7 ǐߜZ5?[C`vr;Q8mi0_ȋ|)@X(˭1_k3n3+- 6 Z( "ol~ "-J:ZlQj -ٲԮB-Z, ]ˮ1DBfr]KPvG-VFKPٚ.0D@lUjm3UZ0֥vvj<,3:z"^yC[ܮ2ڹ 1 ۶v/ץvjj1ڙmLwq:|*&hXs2ig-60[_IgI-ma5Z< fq܊;ovdLT?Ek8M0 zP.Y,~mgF>EJDqJۃ>DrGAۅ>CML͏Yٮa>gVZsSTԐrnsT5y>3Z4_fw6fFI=ࢦ`BCۑaLCb6M^Ʊkq ͥM8 nj5=+(`MhsG`h lb"|ݵy`kmY>C 2dҶ2 GS6k۠mf&PXn0h{0 ژnA¤NKD^*m@ 's:T.vb֊jfZJf#*L}N?ECۍ[ %m*+W@c,5vѦF`ZQFwq%",tTF'#[ }M#,t{(uA"C՚?gKר yB4EM1K}V#"Q#5`*bW9wL?jk0l:/" 6o~8HMS{NSV7yD:!bes+X3ӥ6 YmS1Q1e·c44u+0~}{=Y3O`sm@\i^o+5'C41P4z>m0SP5&Ƨ9h \/E@C5`NQ9@@>,d[SWlk4f\3%fw@+mٯM WF f4xmB&Z^eV)h0~ [Wav G5dHM\ӯJn+ʹév 4u?(ڨڨjJZ"nGSɖ>hЄ44u.[vjx'>~j)phjjwP͝.M) S&\-Fߗ~ܷ4?s]0ʉEBr? ū& zC=+l8-7j4>PG4q;6ٻ$hڈoSLz?BXho-Zl&zon"f2!@]r V0鋶2JC}ծq5x %h[KQ. h3Fe:nqxl@V^0m49svY}GSRE 1v5RÞ[0 Pћ;mJS.LϦ`wk=ZN#>A3N-FjVGZOP 崶& \:?sjм '㩝ߨy83BR~Kj!7z0SBϤ z,SBe9e99yHgIё Cj]~t_L:N3̣:)4B;YH 3zVh!R߶D=i#cƵBGjP;/vCIjP;1?3CKjS;3ݤ7SCMj;S;5/sCOjR;7'CQj;R;9=C__y~tAZZ[tJ >}Ep|="D<#{WIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|wDdP   S ,A img58 bXL[A`5jZnXL[A`5PNG  IHDR lܒPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712Hs,IDATWc 0(H  a3Tc0+@$ae{kIENDB`wDdP   S ,A img59 bXL[A`5^nXL[A`5PNG  IHDR lܒPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712Hs,IDATWc 0(H  a3Tc0+@$ae{kIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|wDdP  S ,A img60 bXL[A`5dnXL[A`5PNG  IHDR lܒPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712Hs,IDATWc 0(H  a3Tc0+@$ae{kIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Ddp;P  S ,A  img61bP}t]u۾f{nP}t]u۾fPNG  IHDRPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712Hs:IDATHKU! QHJeѓv6$ama0> ]c_U9zVqCY[ŧwyA_ƽHU&sf;=S^Gx4PEq 'R dZG U5C@Y8\g?vAK`Ip;}Y )S<<9BFR[fgfЕ,cǷ e`w/[bfw<(Jo="4eRcn^q2)/{}C=*B߶VyWjndeպqumP% w4IENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dd;P  S ,A  img62bVxnw%)ztnVxnw%)ztPNG  IHDR7PLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712Hs9IDATHK D6!imW| H/2k!ѯs\_:*SG(*aSv)x8^9oswo{ɛ0ַwAWn4EFZa۳)` K3~\(rXjp9S'z :z=1 5 *)@]f>"Pf^9Ƚ3P}YC\Jnd:W?"P2 K>ρ'4nʄ<^Hj0\N*m ՂF5Ğ45#f8?i2?[ _(IENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dd;P  S ,A  img63b`-q* }.*2Ꮰo0<n4-q* }.*2Ꮰo0PNG  IHDRo@PLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKKD҂4,Hk{wvw~u,`ha  &k nlHBvy!@ a ̎;O!0|zR5(~rX&UV~)$~ɅUS:4ȒJK,_$ԈP`}U*xAd@cL {/EIݏ`DIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dd;P  S ,A  img64bnY,F(S;JhnBY,F(S;PNG  IHDRdBPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKT[ C,dCJ?`\T>)=%&x{?zEPKKOٙ7& @ ; A\HB @Pyd67QU>C&JͫTXi(S1@[b:)o"s Ob[،OªUYdqqcs9.ҽ%牤k&7 AwVIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dds;P  S ,A  img65bvv]O2Q"HR$nJv]O2Q"HPNG  IHDR]PLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKTI0v)[RspCL*ۗ?|ȓqqn BuEY{\n+ }GJAP9je`!:[R 0!czҠ6"X.6i8 (RPG+ ~aw 3Ҵ𢤣./+xZ]+v{]/;uZ;j$IENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dds;P  S ,A img66bj#']|Fn>#']|PNG  IHDR]PLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKK Cm Sn:u'>!X[VN'$JkD XźY]a$BCZ'£@9Q=}So{8i ^rO!*ԁ:EhC0!JDu D(B(ʎ~M;GNʥ "߶Ԇ`wlٟOO]48IENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Ddd;P  S ,A img67bk.'vdnGn?.'vdnPNG  IHDR\fyPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKT ـvWdFl!w5y>?:$\_!ca~uAt a[-56^GFf5,.,mpAĻt\(wY,TKNBAwia6LXZqcԬØqkWj 2 6KfJZn*%uoIENDB`S$$If!vh#v":V 6,5x34 yt|S$$If!vh#v":V 6,5x34 yt|Dd;P  S ,A img68bR%k^vcH.Yn&%k^vcHPNG  IHDR_QPLTE˙33f3333333333f33333f3f3fffffff33f̙̙33f̙̙33f33f33333f3333333)))333f333333333333333BBBf3333333333f33f33f3ff3f3f3f3f333333f333̙3̙333333f333̙3̙333333f3333333333f3333333f33333f333333333f33333f3f3fffwwwfff3www̙|33f̙̙3̙3̙f̙̙̙̙̙̙3̙3̙f̙̙̙̙̙33f̙̙33333f3̙3̙33333333f3̙3̙333f3f3fff̙f̙fff33f̙̙̙̙33f̙̙̙̙33f̙̙𠠤bbKGDH cmPPJCmp0712HsIDATHKU DDutT†LV.:K>?6Dj,XX`xW .Z.o;1>q,a5?= X$ 3tyGF _QUo0N~e}%U󌀓_W=_>ϓ'pKV-N*|hڪU y__]1⨉Hqp-v3O!ă_ǵ6}Vl%iF_)MUu=ͣ?1gbL>2n+Jf3|Yy/@D-i|LOمvWƛ=vV^K9N7@y|e~]C3`/_Y]~k12'ߥFv:_ ~?=WSgS7K?e~OJ=?q۪g?k(>~yu?+'{c 19\Us=?M >߹^P~z4s1z*nM zV~u7u] ]MG gT䯼5FEMcA+ lE*>tg_q?s(v 4n"M,8xFׁ"?@Ư = (+¯믘Pen?qhSZlcE|+8?6/'#(2t%ƯP &d1/'/P5VBj6QS="ެQɟԀ)['x]~::UpXh =` ?$~ =`(?Ul??M~|P6yޛ`~YOH4!9qAf]Y{K(ڎM/ SOP cewuOECV 0?UKď@ }T8_Օ:"~ rB?@_!N<v[Y [ePBl:5_ ϸQ$'(4o`aA,YDs00P_H4P)c$Ġd/,l~ z@WEs>TcOlw ! ZpUY;_cylies~vc1mH`D=b~zKpzb^HG6伙K?ۑSd%t%09r{#Dt7[L|X3WE0 CrdO^"?GcaQRNϛo@"?d/dZL;)C@%'=ka_c?\+9P?dZLn*_hKapNKSRvbg?Qd?ddˉ,zd?\c|(x]w?P?KzNUZ*:̑#??\xWdZe'/FTZ66{ЦХ@dgZ{U!`2-&;*|v C}1TӘ+"DQcV.Ç +R/l.d" 9λCG{ń$e`wFd-&`$oՕ6w uui {t~a_Ύ?yb0b޿~ p 0(C"3> lM2/<s"3oF||Pd 0O8$P?'Sig<(Uf_@~z´lυ"xY划 b ?}@;C>TG;+B̝O7$~*]SWYqLg36AoU(u9=1P 5+{@ШK>,7c[!]UpIY&`b+ߜ! #v+_|b(!% yF+BKV-VRrYH~>wv$z4g-f`?_W[xk:gW8qt\\*?0+"?؀ݣjuptb#Sv7`T>Ry+p~d%T`K&rrT8k1p 0ީQ4[ħ4Ha5m -Ñ6!ںf)Y3Fɐ7 €rUҼ0V̱ѐ7Q;urB0J߆oɐWZ5Òώo ;P~Hob"4 `oB63j&;PGGzt4lݶ$` @T-;prTMD&r<%  7?_|3G|\KZvb /ܩ|vKgP@2!fX*Oa}0N 9I^/QqnC$xK~l em@5[R|ܙR%hDSc=W:<o.L6A_ʄ)[UDs̓_MǕ?!0Ds 6~MRr e-9ҬI -Cn_m_>j(~D \m@ѿs}͝,W7]4)k04^έ"ߢr;Y-?Ϟ5<6kcoXI-Z/)qFqG= hSc+j@wO0k>V~t^CU:p^^Grl>8ZܙhwZl' )W *8QT5˼y.:*Ř(R f ?͟mjc?EI"\%t?Vpc_4Kf?@qEb}d R&3!Ջ3~+_h[W YyO ۞h?idSrс)oXWݒv)~TEȗ3X?Q*?C‡=^XMհ-O~T//48@MIiD𙵘$~_D24~ !a^4x qR|ooЛIrSuf%6eDÕ.uA g6%L"OLdե3B<ǚ2utl\w~, m' eƎ:MJ+į,tcWDYx~LQvG%V7*HA eqre3+lJqiԯ߀;yX':%P#YV]eVR_5*? >'Q&^4QbtYd$$9:/'ȧ{6-&E~) 1i҇:$]DRRޜ@gtp2-&70)yY}l5<2K.Ê'ӑ&t|,GUWŕ/hĞ))} +OUhxK.@oI'{Lkϐ>y$l'QGWXjj 3%LOWAOJL+h7Mlk2V+OwwCHV[8Wǜo| W>z 0L Zvjgbݵpb#b7>>Es;5X r6=;gTL8#H"N,A4zYUp|l1/Fm3"Kl qðTSSv_!}?4AKڜ,ij1~J=u(~>`4Iv RoI,^;k}s r-_'b,c @螫̾MYyL< 0lϲgWALD /s*-ƦyաQcH _/Ƞ 30LiaMB%)<~7'C{D ǬgbNLߴ\L' ~;iг%EWLJl*S6u@xe=EY"?.j[߻&O鴅%e̦>|1 &1V)]8`+Z O3a< * ߬ 8in٫׾}G$> xx?DVȢS]U1 s!f%PO_'[̢R> wt;&6o1wpM| XDQ-2[Jp]|KhJ[KZ$&YL'^4^Mn0*" 5 ArmYRHG=aEf) ar Oo(-f~&#z5_(߂ (OH#9+}G0>8C"ZF-6XI+L>'́1MNxr ~|)S8lS~C !+_rHwppr{R^ctQ[hTw ʘ^d9?SEJ?AIoy f Ef; ~;߲ I5)iRn]&DYZ`kȄ{W-f'~k+S믳^P=exW63@w,2ۍPͽ8YYIFSَiujĦwsݕ81|0KٙDs 'LaS&HfEU*`NR0/ m"gzՖ.*>hobA9 o!F ?֐OsѳlO%o!f% B.;ȏѳ>a2a87mhch5tR#%HW~@Yv˜ 0CQ;Vʷ6>ܶX~lԍ_epĦS zNɌ Ez,])I=fL"xY[g'ʇ,Ok~vQ'>s﷩hh}X L O k"#TF7P$v-} Y*AmŒcE[aOm@&2W(2?:q9^i1Ƞc%0EyQ|1)jZ1#Xa=I~<ğ]z*ߊC^.ן+=Zan?-Sl7s˶K'GsJͯhplڿ*VXm.Q(*>U|!.?d| jD\FwtxZ7UJ7(>G -]VXh4WݱƜg\ q҅ c" }3"fHn"ґ&ݔ M/]ɚG:]E;LYŠ%\p!a#_Ȕa{#57Y-ScO]).?ݴ:\GMg x `Wڅln `wu@͸ܺ1^ uգ0ʅ C(ݛ_yOQcw DuZnV- %5lkðA C&~lw,gbXB ͑YO bZ3}un7?Tzbv;Ehx6/s UX }d_!ݴ-)pS~vX0.ԴwacoF <m3.dn5۠RmHl`3MM px=e{u"~'V[A4xlw,~p.%vą tAyKհw7M*U}MB _{ÏZ &+cD%DWvķ?r~ÅBPJ(24hѭ.o*=֭"+&5+0?X.B:n~Ub҄BM٭bn:}ri^Cw\*j,s^HsZf/igX'Amíbn:~8SdMkw~X??ヶ6u!-^]Hs'тn* `W۟1hwNCf=/4rB~FЕ.wF~}J2䧕qJ~[-2/|Pk?$O9i>8SgoK5(*f.rZ~qRJkn&Q8 imhEwLP8ܺ=~Kz!`WN\&~m }UNr;u@hXFqcsBG$%г Il~cYgק 4uHnXRʶS}Lezx D8Cp1VO/QӰ~aYTMcE}YdMrW: O+]˜ߔHtPs#YYg7iZF:,Os3RԩIrX0YJm{r `С-;c=1g~'}xPiB$IO1Êk9IcLHY<;*v7'aE\h>=^,*8q;^*4?Wq{nԉogAߤ>8f2*<")QHxK |]Zz)ӁMSm@\&>!7;wP3[EBU`1OC5VD Xa?p S4[NS28;Y[꫙,T1|n;+/ʕj\\,E:! t4.T̡ e1 }; [z^pl@ok0e g@GGHPXNT,مde|*YdT\Y䀰+(T7$ow2缂#G֛ʥ?q NK-/M,WgxFV/FQⷶO&ecx\QLW@H!+{[|{!KAi `cm2iU|Y+ ި [[vxrNE3pmR =Y04,!&0+WC܃@oOS2'Sٮ05$ɤ]pm3Ft GɄ-!y"ӉV . `עv,O.%вKasSƭvMz`3{9+e@eՔLy7W_XtlPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-!pO[Content_Types].xmlPK-!֧6 -_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!!Z!theme/theme/theme1.xmlPK-! ѐ'( theme/theme/_rels/themeManager.xml.relsPK]# t*? h :ETd3!9$K(*Q,R/1t3!%*.46;GMTZ^ci  j k ?7tx61 q !!"""5#<$$7%%J'=(((w))9**+P,--1.E.V/0E00032P2(3G3r3t3 "#$&'()+,-/01235789:<=>?@ABCDEFHIJKLNOPQRSUVWXY[\]_`abdefghjklmn?gi/ 1 7 9 ; O P R   , moSUln68:@ 5!7!=!!!!?"A"G""""I#K#n####o$q$%R&T&e)))t*CCCCCCCCCCCCCCCCCCCCCCCCCC=?UW ^fQYv*5<=?>APUz8 9 ! GIjvz{  { g#l#''&(+(7)8)Q)R)v*::::::::::::::::::::: Jlqs|D'|u*t*v*@s*s*j 0s*s*(t*x@xx @UnknownG*Ax Times New Roman5Symbol3 *Cx ArialA$BCambria Math"qhj'j'V$MV$M!24_*_*3IP)?*2!xx ,=Graphical Method of Solution of a Linear Programming Problem testHossein Arsham Oh+'0( @L p | '@Graphical Method of Solution of a Linear Programming Problem test Normal.dotmHossein Arsham2Microsoft Macintosh Word@G@7Qc@7QcV$ ՜.+,D՜.+,|8 hp  'University of BaltimoreM_* >Graphical Method of Solution of a Linear Programming Problem Title 8@ _PID_HLINKS'AD9Yh img477Y0img49>Ximg50?X:img51<Ximg52=XQimg53:Ximg54;X img558Xn img569X img576X img587XT img59>[mimg60?[#img61<[9$img62=[$img63:[6*img64;[*img658[@+img669[+img676[J,img687[,img69>Zp-img70?ZS/img71<Z2img72  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnoqrstuvwxyz{|}~     Root Entry F 9^cData px1TableWordDocument.SummaryInformation(DocumentSummaryInformation8CompObj` F Microsoft Word 97-2004 DocumentNB6WWord.Document.8