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 PackProduction QuantityPT-100200,000PT-200100,000P T-300150,000Photon 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:PlantProductPhilippinesMexi coPT-100$0.95$0.98PT-200$0.98$1.06P T-300$1.34$1.15The 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 $0.12 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. LetP1=number of PT-100 battery packs produced at the Philippines plantP2=number of PT-200 battery packs produced at the Philippines plantP3=number of PT-300 battery packs produced at the Philippines plantM1=number of PT-100 battery packs produced at the Mexico plantM2=number of PT-200 battery packs produced at the Mexico plantM3=number of PT-300 battery packs produced at the Mexico plantMinP1+P2+P3+M1+M2+M3 s. t. P1+P2+P3+M1+M2+M3= Production PT-100P1+P2+P3+M1+M2+M3= Production PT-200P1+P2+P3+M1+M2+M3= Production PT-300P1+P2+P3+M1+M2+M3≤ Capacity Phi PT-100 & 200P1+P2+P3+M1+M2+M3≤ Capacity Mex PT-100 & 200P1+P2+P3+M1+M2+M3≤ Capacity Phi PT-300P1+P2+P3+M1+M2+M3≤ Capacity Mex PT-300P1, P2, P3, M1, M2, M3 ≥ 0 (b)Solve the linear program developed in part (a), to determine the optimal production plan. Qty ProducedPhillipinesMexicoPT-100 PT-200 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.