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Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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(b) | Solve the linear program developed in part (a), to determine the optimal production plan. If the amount is zero, enter "0". | ||||||||||||||
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Total Cost = __________$ | |||||||||||||||
(c) | Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional 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 production and/or shipping cost per unit would have to change to produce additional units of the PT-200 in the Mexico plant. | ||||||||||||||
If required, round your answer to two decimal digits. | |||||||||||||||
At least $ _______/ unit. |

Transcribed Image Text: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 production quantities:
- **PT-100:** 200,000 units
- **PT-200:** 100,000 units
- **PT-300:** 150,000 units
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 due to differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are listed below:
| 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 $0.15 per unit, and from the Mexico plant is $0.12 per unit.

Transcribed Image Text:**Linear Programming for Battery Pack Production Optimization**
Photon Technologies needs to determine the optimal number of battery packs to produce at each plant to minimize production and shipping costs. To achieve this, a linear program model is being developed.
**Variables Definition:**
- **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
**Objective:**
- Minimize the total number of battery packs produced: P1 + P2 + P3 + M1 + M2 + M3
**Subject to Constraints:**
1. **Production Constraints:**
- \( P1 + M1 =\) Production PT-100
- \( P2 + M2 =\) Production PT-200
- \( P3 + M3 =\) Production PT-300
2. **Capacity Constraints:**
- \( P1 + P2 + M1 + M2 \leq\) Capacity for Philippines PT-100 & 200
- \( P1 + P2 + M1 + M2 \leq\) Capacity for Mexico PT-100 & 200
- \( P3 + M3 \leq\) Capacity for Philippines PT-300
- \( P3 + M3 \leq\) Capacity for Mexico PT-300
3. **Non-negativity Constraints:**
- \( P1, P2, P3, M1, M2, M3 \geq 0\)
This linear program will help Photon Technologies decide on the number of units to produce at each location while minimizing associated costs.
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