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$0.10 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 | = | Â Â | 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 | | | | | | | | | |
