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Chapter 12 Assignment Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models o 3. lithium-ion battery packs for a new line of phones. The contract calls for the following: 4. Battery Pack Production Quantity 5. 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 dif 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 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 plan 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 th 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 Chapter 12 Assignment 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. 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 + 1.13 1.15 + x + + + 1.23 1.23 1.15 1.23 P1 P2 P3 M1 M2 M3 s.t. + + + 1 + 0 o 1 0 200000 % Production 0 P1 P2 P3 M1 M2 M3 + + + + + 0 Production Pla 0 + 1 0 1 0 100000 P1 P2 P3 M1 M2 M3 + + + + + 0 0 1 0 0 Production PT-300 1 15000C P1 P2 P3 M1 M2 M3