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
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
100%
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Solve the linear program developed in part (a), to determine the optimal production plan. | |||||||||||||||
|
|||||||||||||||
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.
|
Solution
by Bartleby Expert
Follow-up Question
which one would be the optimal production plan for part b?
Solution
by Bartleby Expert
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.