(b)Solve the linear program developed in part (a), to determine the optimal production plan. If the amount is zero, enter "0". Qty Produced PhillipinesMexicoPT-100 PT-200 PT-300 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. 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 unitsPhoton 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. **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-3002. **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-3003. **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.

PLEASE BE NOTED AS PER THE POLICY I HAVE SOLVED THE FIRST THREE SUB-QUESTIONS. PLEASE POST ANOTHER PART SEPARATELY. Given, Battery Pack Production Quantity PT-100 200,000 PT-200 100,000 PT-300 150,000a) Linear program model: Decision variables: Let P1 = Number of PT-100 products in the Philippines P2 = Number of PT-200 products in the Philippines P1 = Number of PT-300 products at Philippines M1 = Number of PT-100 products at Mexico M2 = Number of PT-200 products at Mexico M3 = Number of PT-300 products at Mexico Objective: Min (0.95+0.15)P1 + (0.98+0.15)P2 + (1.34+0.15)P3 + (0.98+0.08)M1 + (1.06+0.08)M2 + (1.15+0.08)M3 or, Min 1.10P1 + 1.13P2 + 1.49P3 + 1.06M1 + 1.14M2 + 1.23M3 s.t. P1 + M1 ≥ 200,000 P2 + M2 ≥ 100,000 P3 + M3 ≥ 150,000 P1 + P2 ≤ 175,000 M1 + M2 ≤ 160,000 P3 ≤ 75,000 M3 ≤ 100,000 P1, P2, P3, M1, M2, M3 ≥ 0 (b) Excel solver using linear programming Formula: H2 =SUMPRODUCT(B2:G2,$B$11:$G$11) copy to H2:H9 Optimal Solution: Decision Variable Value P1 40000 P2 100000 P3 50000 M1 160000 M2 0 M3 100000 Total production and shipping cost = $ 524,100 The sensitivity report is as follows Referring to the above sensitivity analysis, (c) Cost will reduced in objective coefficient of P1 is 0.04 therefore production and/or shipping cost per unit has to decrease by $ 0.04 to produce additional units of PT-100 in Philippines plant.