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 Pack	Production Quantity
PT-100	200,000
PT-200	100,000
PT-300	150,000

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:

	Plant
Product	Philippines	Mexico
PT-100	$0.95	$0.98
PT-200	$0.98	$1.06
PT-300	$1.34	$1.15

(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 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 3 + 32 + 33 + v + M2 M3 s.t. 3 + 32 + 33 + v + M2 M3 = Production PTlOO 3 + 32 + 33 + v + M2 M3 = Production PTZOO 3 + 32 + 33 + v + M2 M3 = Production PT300 3 + 32 + 33 + v + M2 M3 5 Capacity Phi P11003200 3 + 32 + 33 + v + M2 M3 5 Capacity Mex PT-lD&200 3 + 32 + 33 + v + M2 M3 5 Capacity Phi PT300 3 + 32 + 33 + v + M2 M3 3 Capacity Mex PT-3DCI P1, P2, P3, l\"l21.l'v'l2r ['13 2 0 h) Solve the linear program developed in part (a), to determine the optimal production plan. If the amount is zeror enter 0 Qty Produced Phillipines Mexico PTlOO 400,00 160,00 PTZOO 100,00 0 PT300 50,000 100.00 Total Cost = 3; c) Use sensitivity analysis to determine how much he production andx'or shipping cost per unit would have to change to produce additional units of the PTlDO in the Philippines plant. If required, round your answer to two decimal digits. At least 3; ,r' unit. d} Use sensitivity analysis to determine how much the production andx'or shipping cost per unit would have to change to produce additional units of the PTZDO in the Mexico plant. If required, round your answer to two decimal digits. At least 3; ,r' unit