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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. Battery Pack Production Quantity PT-100 PT-200 PT-300 PT-100 PT-200 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. Product Philippines Mexico $0.98 PT-300 s.t. PT-100 Production $0.95 PT-200 Production $0.98 PT-300 Production $1.34 202,000 101,000 149,000 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 (in dollars) associated with the new contract. (Assume P, number of PT-100 battery packs produced at the Philippines plant, P₂- number of PT-200 battery packs produced at the Philippines plant, P, 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, My number of PT-300 battery packs produced at the Mexico plant.) Min $1.06 PT-300 Production Mexico Plant $1.15 Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant PT-300 Production Philippines Plant M₂ M₂ M₂ P P₂ P₂ 20 (b) Solve the linear program developed in part (a) to determine the optimal production plan. (M₂, M₂, M₂, P₂, P₂, P3) - ( What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.)

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. Battery Pack Production Quantity PT-100 PT-200 PT-300 PT-100 PT-200 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. Product Philippines Mexico $0.98 PT-300 s.t. PT-100 Production $0.95 PT-200 Production $0.98 PT-300 Production $1.34 202,000 101,000 149,000 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 (in dollars) associated with the new contract. (Assume P, number of PT-100 battery packs produced at the Philippines plant, P₂- number of PT-200 battery packs produced at the Philippines plant, P, 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, My number of PT-300 battery packs produced at the Mexico plant.) Min $1.06 PT-300 Production Mexico Plant $1.15 Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant PT-300 Production Philippines Plant M₂ M₂ M₂ P P₂ P₂ 20 (b) Solve the linear program developed in part (a) to determine the optimal production plan. (M₂, M₂, M₂, P₂, P₂, P3) - ( What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 30P
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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. Battery Pack Production Quantity PT-100 Min PT-200 s.t. PT-300 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. PT-100 PT-200 Product Philippines Mexico PT-300 PT-100 Production $0.95 PT-200 Production $0.98 PT-300 Production 202,000 $1.34 101,000 149,000 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 can use to determine how many units of each battery pack to produce at each plant to minimize the total production and hipping cost (in dollars) associated with the new contract. (Assume P₁ = number of PT-100 attery packs produced 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.) PT-300 Production Mexico Plant $0.98 $1.06 $1.15 Combined PT-100 and PT-200 Production Mexico Plant PT-300 Production Philippines Plant M1, M2, M3, P1, P2, P3 20 Combined PT-100 and PT-200 Production Philippines Plant (b) Solve the linear program developed in part (a) to determine the optimal production plan. (M1, M2, M3, P1, P2, P3) = What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $
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. Battery Pack Production Quantity PT-100 Min PT-200 s.t. PT-300 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. PT-100 PT-200 Product Philippines Mexico PT-300 PT-100 Production $0.95 PT-200 Production $0.98 PT-300 Production 202,000 $1.34 101,000 149,000 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 can use to determine how many units of each battery pack to produce at each plant to minimize the total production and hipping cost (in dollars) associated with the new contract. (Assume P₁ = number of PT-100 attery packs produced 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.) PT-300 Production Mexico Plant $0.98 $1.06 $1.15 Combined PT-100 and PT-200 Production Mexico Plant PT-300 Production Philippines Plant M1, M2, M3, P1, P2, P3 20 Combined PT-100 and PT-200 Production Philippines Plant (b) Solve the linear program developed in part (a) to determine the optimal production plan. (M1, M2, M3, P1, P2, P3) = What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $
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Follow-up Question
Solve the linear program developed in part (a), to determine the optimal production plan.
 
  Qty Produced
  Phillipines Mexico
PT-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.

 
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Follow-up Question

I am not sure why i got it marked incorrect

= (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 (in dollars) associated with the new contract. (Assume 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 1.13P1 + 1.16P2 + 1.52P3 + 1.08M1 + 1.16M2 + 1.25M3 s.t. PT-100 Production PT-200 Production PT-300 Production Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant PT-300 Production Mexico Plant PT-300 Production Philippines Plant M₁, M2, M3, P1, P2, P3 20 P1 + M1 > 202,000 Enter an equation. P2 + M2 ≥ 101,000 Enter an equation. P3 + M3 ≥ 149,000 X Enter an equation. P1+ P2 ≤ 175,000 Check which variable(s) should be in your answer. M1 + M2 ≤ 160,000 X Check which variable(s) should be in your answer. P3 ≤ 75,000 X Check which variable(s) should be in your answer. M3 ≤ 100,000 Check which variable(s) should be in your answer.
Transcribed Image Text:= (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 (in dollars) associated with the new contract. (Assume 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 1.13P1 + 1.16P2 + 1.52P3 + 1.08M1 + 1.16M2 + 1.25M3 s.t. PT-100 Production PT-200 Production PT-300 Production Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant PT-300 Production Mexico Plant PT-300 Production Philippines Plant M₁, M2, M3, P1, P2, P3 20 P1 + M1 > 202,000 Enter an equation. P2 + M2 ≥ 101,000 Enter an equation. P3 + M3 ≥ 149,000 X Enter an equation. P1+ P2 ≤ 175,000 Check which variable(s) should be in your answer. M1 + M2 ≤ 160,000 X Check which variable(s) should be in your answer. P3 ≤ 75,000 X Check which variable(s) should be in your answer. M3 ≤ 100,000 Check which variable(s) should be in your answer.
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Follow-up Question

which one would be the optimal production plan for part b?

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Follow-up Question
(c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-100 in the Philippines plant. It would have to decrease by more than $ per unit. (d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-200 in the Mexico plant. It would have to decrease by more than $ per unit.
Transcribed Image Text:(c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-100 in the Philippines plant. It would have to decrease by more than $ per unit. (d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-200 in the Mexico plant. It would have to decrease by more than $ per unit.
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