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 bater manufacturing plant are as follows: capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.21 per unit, and the cost of shipping from the Mexico plant is $0.18 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. If the constraint is one, enter "1". If the amount is zero, enter "0". Let P1= number of PT100 battery packs produced at the Philippines plant P2 = number of PT-200 battery packs produced at the Philippines plant P3= number of PT300 battery packs produced at the Philippines plant M1= number of PT100 battery packs produced at the Mexico plant M2 = number of PT200 battery packs produced at the Mexico plant M3= number of PT300 battery packs produced at the Mexico plant Production PT-100 (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 dig. 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 \$ / unit. 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 bater manufacturing plant are as follows: capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.21 per unit, and the cost of shipping from the Mexico plant is $0.18 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. If the constraint is one, enter "1". If the amount is zero, enter "0". Let P1= number of PT100 battery packs produced at the Philippines plant P2 = number of PT-200 battery packs produced at the Philippines plant P3= number of PT300 battery packs produced at the Philippines plant M1= number of PT100 battery packs produced at the Mexico plant M2 = number of PT200 battery packs produced at the Mexico plant M3= number of PT300 battery packs produced at the Mexico plant Production PT-100 (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 dig. 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 \$ / unit