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 needs the following quantities to be finally produced:
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 each of the plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced (combined). 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 $0.21 per unit, and the cost of shipping from the Mexico plant is $0.08 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 cost (including both production and shipping costs) associated with the new contract. To deal with combining costs, first determine if one specific type of battery is produced and shipped from a specific plant, how much would be the total cost. Then proceed to the problem formulation below.
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
Answers: 1
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