Please help, thank you!
Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract With a large electronics manufacturer to produce three models of lithiumeion battery packs for a new line of phones. The contract calls for the followmg. Battery Pack Production Quantity PT7100 202,000 PT7200 102,000 PT7300 148,000 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. Product Ph Ippines Manon P'FlOCI $0.95 $0.90 PT'ZOCI $0.98 $1.06 PT-300 $1.34 $1.15 The PT7100 and PT7200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT7100 and P'FZOO battery packs produced. The combined PT7100 and PT7200 production capacities are 175,000 units at the Philippines plant and 160,000 Ul'lllS at the Mexico plant. The P'F300 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 $0.10 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 m imize the total production and shipping cost (in dollars) associated with the new contract. (Assume P1 = number of PTelDO battery packs produced at the Philippines plant, P2 = number of PT7200 battery packs produced at the Philippines plant, P3 = number of PT73DD battery packs produced at the Philippines plant, M1 = number of PT-100 battery packs produced at the Mexico plant, M2 : number of PT-200 battery packs produced at the Mexico plant, M3 : number of PT-300 battery packs produced at the Mexico plant.) Min X s.t. PTelDO Production X PTeZDO Production X PT7300 Production X Combined PT7100 and PT7200 Production Mexico Plant Combined PTelCIO and PTeZOG Production Mexico Plant X Combined PTlCIO and PTZOG Production Philippines Plant X PT300 Production Mexico Plant X PT300 Production Philippines Plant X M1, M2, M3, P1, P2, F3 2 0 (h) Solve the linear program developed in part (a) to determine the optimal production plan. (M1,M2,M3,P1.P2. P3) =( ) x What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $:x (c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT7100 in the Philippines plant. It would have to decrease by more than $ |: x per unit. (d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PTeZDO in the Mexico plant. It would have to decrease by more than $ |: X per unit
