please answer questions A, B, C and D

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: 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: 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 capacties are 75,000 units at the Philippines plant ant 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is 50.21 per unit, and the cost of shipping from the Mexico plant is 50.18 per unit. (a) Develop a linear propram 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 assodated with the new contract. If the constraint is one, enter " 1 ". If the amount is zeto, enter 0. Let P1 - number of PT-100 battery packs wroduced at the Philippines plant P2 - number of PT-200 batterv packs produced at the philinpines plant P3 - number of PT-300 battery packs produced at the Hillippines plant M1 - number of pr-100 battery packs produced at the Mexico plant M2 - number of pr-20n battery packs produced at the Mextico plant M3 - number of PT-300 battery packs produced at the Mexico plant (b) Solve the finear program developed in part (a), to determine the optimal production plan, If the amount is zero, enter " 0 ". Total cost = - (c) Use sensitivitv ana vis to determine how much the production and/or shipping cost per unit would have to change to produce additional unit? of the PT-100 in the Phillppines plant. If required, round your answer to two decimal digits. At least 1 / unit: (d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional unit of the pr-200 in the Mexico plant. If required, round your answer to two decimal digits. At least 4 minit