Photon Technologies, Inc., a manufacturer of batteries formobile phones, signed a contract with a large electronicsmanufacturer to produce three models of lithium-ion battery packsfor 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 atmanufacturing plants located in the Philippines and Mexico. Theunit cost of the battery packs differs at the two plants because ofdifferences in production equipment and wage rates. The unit costsfor each battery pack at each manufacturing plant are asfollows:

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

The PT-100 and PT-200 battery packs are produced using similarproduction equipment available at both plants. However, each planthas a limited capacity for the total number of PT-100 and PT-200battery packs produced. The combined PT-100 and PT-200 productioncapacities are 175,000 units at the Philippines plant and 160,000units at the Mexico plant. The PT-300 production capacities are75,000 units at the Philippines plant and 100,000 units at theMexico plant. The cost of shipping from the Philippines plant is$0.18 per unit, and the cost of shipping from the Mexico plant is$0.12 per unit.

(a)	Develop a linear program that Photon Technologies can use todetermine how many units of each battery pack to produce at eachplant to minimize the total production and shipping cost associatedwith the new contract.
	Let P1 = number of PT-100 battery packs produced at the Philippinesplant P2 = number of PT-200 battery packs produced at the Philippinesplant P3 = number of PT-300 battery packs produced at the Philippinesplant M1 = number of PT-100 battery packs produced at the Mexicoplant M2 = number of PT-200 battery packs produced at the Mexicoplant M3 = number of PT-300 battery packs produced at the Mexicoplant
	Min P1 + P2 + P3 + M1 + M2 + M3 s.t. P1 + P2 + P3 + M1 + M2 + M3 = Production PT-100 P1 + P2 + P3 + M1 + M2 + M3 = Production PT-200 P1 + P2 + P3 + M1 + M2 + M3 = Production PT-300 P1 + P2 + P3 + M1 + M2 + M3 ? Capacity Phi PT-100 & 200 P1 + P2 + P3 + M1 + M2 + M3 ? Capacity Mex PT-100 & 200 P1 + P2 + P3 + M1 + M2 + M3 ? Capacity Phi PT-300 P1 + P2 + P3 + M1 + M2 + M3 ? Capacity Mex PT-300 P1, P2, P3, M1, M2, M3 ? 0
(b)	Solve the linear program developed in part (a), to determinethe optimal production plan.
	Qty Produced Phillipines Mexico PT-100 PT-200 PT-300
	Total Cost = $
(c)	Use sensitivity analysis to determine how much the productionand/or shipping cost per unit would have to change to produceadditional units of the PT-100 in the Philippines plant.
	If required, round your answer to two decimal digits.
	At least $  / unit.
(d)	Use sensitivity analysis to determine how much the productionand/or shipping cost per unit would have to change to produceadditional units of the PT-200 in the Mexico plant.
	If required, round your answer to two decimal digits.
	At least $  / unit.