unit. 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 (in dollars) associated with the new contract. (Assume P1= number of PT-100 battery packs produced at the Philippines plant, P2= number of PT-200 battery packs produced at the Philippines plant, P3= number of PT-300 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 s.t. PT-100 Production PT-200 Production PT-300 Production Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant PT-300 Production Mexico Plant PT-300 Production Philippines Plant M1,M2,M3,P1,P2,P30 Solve the linear program developed in part (a) to determine the optimal production plan. (M1,M2,M3,P1,P2,P3)=([] What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $ plant. It would have to decrease by more than $ per unit. plant. It would have to decrease by more than $ per unit