Question: The following LP formulation represents a transportation problem where raw material (in tons) is transported from Supplieri, i=(1,2,3) to Plant j. j={1,2,3). The problem is

The following LP formulation represents a transportation problem where raw material (in tons) is transported from Supplieri, i=(1,2,3) to Plant j. j={1,2,3). The problem is solved and the optimal objective function value is 5200. Using the sensitivity report, what is the optimality range of the cost of transporting 1 ton of the raw material from Supplier 2 to Plant 3? Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 + 4x22 + 4.8x23 + 3.5x31 +3,6x32 + 3.2x33 Subject to 31 + x32 + x33 =500 x11 + x21 + x31 - 500 x12 + x22 + x32 = 700 *13 + x23 + x33 - 600 xijc-200, for i = {2.3) & ;= (1,2,3) xij >0, for i= (1.2.3) & ;= (1,2,3) Variables Name 700 X11 X12 X13 X21 X22 X23 X31 X32 X33 Final Reduced Objective Allowable Allowable Value Cost Coefficient increase Decrease 500 1 2.5 IE+30 3 0.6 1E430 200 5 1E+30 0.2 0 3.5 1E30 2.5 0 4 1E+30 1 200 4.8 002 1E430 0 3.5 1E+30 2.5 0 3.6 1E-30 0.6 200 3.2 1.8 16:30 OOOOOOOOO Constraints Name TOTAL SUPPLY OF SUPPLER SUPPLY FROM SUPPLER 2 TO PLANT 1 Final Shadow Constraint Allowable Allowable Value Price Side increase Decrease 200 0 500 15-30 300 0 0 200 1E30 200 O 0 200 10-30 200 Variables Name X11 X12 X13 X21 X22 X23 X31 X32 X33 Final Reduced Objective Allowable Allowable Value Cost Coefficient increase Decrease 500 0 1 2.5 1E+30 700 0 3 0.6 1E+30 200 0 5 1E+30 0.2 0 3.5 1E+30 2.5 0 4 1E+30 1 200 0 4.8 0.2 1E+30 0 0 3.5 1E+30 2.5 0 0 3.6 1E+30 0.6 200 0 3.2 1.8 1E+30 oo Constraints OOO Name TOTAL SUPPLY OF SUPPLIER 3 SUPPLY FROM SUPPLIER 2 TO PLANT 1 SUPPLY FROM SUPPLER 2 TO PLANT 2 SUPPLY FROM SUPPLER 2 TO PLANT 3 SUPPLY FROM SUPPLIER 3 TO PLANT 1 SUPPLY FROM SUPPLIER 3 TO PLANT 2 SUPPLY FROM SUPPLIER 3 TO PLANT 3 Demand of Plant 1 Demand of Plant 2 Demand of Plant 3 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 200 0 500 1E+30 300 0 200 1E+30 200 0 200 1E+30 200 200 -0.2 200 200 200 0 200 1E+30 200 0 200 1E+30 200 200 -1.8 200 200 200 500 1 500 1E30 500 700 3 700 1E+30 700 5 600 1E+30 200 WOO 600 a. (0.400) b. (3, int) OC (-inf, 5) d. (int)

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