The PT-100 and PT-200 battery packs are produced using similar production equipm

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 175000 units at the Philippines plant and 160000 units at the Mexico plant. The PT-300 production capacities are 75000 units at the Philippines plant and 100000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.18 per unit and the cost of shipping from the Mexico plant is $0.10 per unit.a. Develop a linear program that PhotoTech can use to determine how many units of each battery pack to produce at each plant in order to minimize the total production and shipping cost associated with the new contract.b. Solve the linear program developed in part (a) to determine the optimal production plan. c. Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change in order to produce additional units of the PT-100 in the Philippines plant.d. Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change in order to produce additional units of the PT-200 in the Mexicoplant.