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

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 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 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 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.

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 plan

M3 = number of PT-300 battery packs produced at the Mexico plant

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