Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line of phones. The contract calls for the following Battery Pack PT-100 PT-200 PT-300 Production Quantity 200,000 100,000 150,000 Photon Technologies can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows: Plant Product PT-100 PT-200 PT-300 Philippines $0.95 $0.98 $1.34 Mexico $0.98 $1.06 $1.15 The PT-100 and PT-200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.15 per unit, and the cost of shipping from the Mexico plant is 0.08 per unit. (a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost associated with the new contract. Let P1number of PT-100 battery packs produced at the Philippines plant P2 number of PT-200 battery packs produced at the Philippines plant P3 number of PT-300 battery packs produced at the Philippines plant M1number of PT-100 battery packs produced at the Mexico plant M2 number of PT-200 battery packs produced at the Mexico plant M3number of PT-300 battery packs produced at the Mexico plant (a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost associated with the new contract. Let P1 number of PT-100 battery packs produced at the Philippines plant P2 number of PT-200 battery packs produced at the Philippines plant P3number of PT-300 battery packs produced at the Philippines plant M1number of PT-100 battery packs produced at the Mexico plant M2number of PT-200 battery packs produced at the Mexico plant M3number of PT-300 battery packs produced at the Mexico plant Min 1.10 P1.13 P1.49 P3 1.0s M 1.14 OM2 1.23 M3 P2 + M1+ s.t P1+ M3 200000 M3 1o0000 M3150000 17500 P2 + P3 + M1 + M2 + Production PT-100 P1 + P2 + P3 + M1+ M2 + Production PT-200 P1 + P2+ P3+ M1 + M2 + Production PT-300 Capacity Phi PT-100 & 200 Capacity Mex PT-100 & 200 Capacity Phi PT-300 Capacity Mex PT-300 P1 + P2+ M1 + M2+ P1 + P2+ P3 + M1 + M2+ M3 S 160000 P1 + 3M3 75000 P2 + P3 + M1 + M2 + P1 + M3 100000 P2 + P3 + M1 + M2 + P1, P2, P3, M1, M2, M3 2 0 (b) Solve the linear program developed in part (a), to determine the optimal production plan. Qty Produced Phillipines Mexico PT-100 16000c 40000 PT-200 100000 0 5000 1000 PT-300 Total Cost-$ (c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-100 in the Philippines plant. If required, round your answer to two decimal digits At least $ / unit. (d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-200 in the Mexico plant. If required, round your answer to two decimal digits. At least $ .05/ unit.
