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Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items. Demand Production Cost Production Capacity MIN: Subject to: Inventory Month 1 Inventory Month 2 Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how many of each appliance to manufacture during each of the next four months to meet the expected demand at the lowest possible total cost. (Let P, number of units to produce in monthi and I, - inventory held at the end of month i.) Inventory Month 3 Inventory Month 4 (a) Formulate an LP model for this problem to minimize total cost (in dollars). (Enter your answers for production as a comma- separated list of inequalities and/or equations.) Production Month 1 Production Month 2 1 410 $49.00 510 Production Month 3 Month Production Month 4 4, v 2 590 $45.00 510 3 300 $46.00 440 4 550 $47.00 560 (b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? (P₂ PyPy Party lady la)-([ (c) How much money (in dollars) could Acme save if they were willing to drop the restriction about producing at least 400 units per month?

Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items. Demand Production Cost Production Capacity MIN: Subject to: Inventory Month 1 Inventory Month 2 Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how many of each appliance to manufacture during each of the next four months to meet the expected demand at the lowest possible total cost. (Let P, number of units to produce in monthi and I, - inventory held at the end of month i.) Inventory Month 3 Inventory Month 4 (a) Formulate an LP model for this problem to minimize total cost (in dollars). (Enter your answers for production as a comma- separated list of inequalities and/or equations.) Production Month 1 Production Month 2 1 410 $49.00 510 Production Month 3 Month Production Month 4 4, v 2 590 $45.00 510 3 300 $46.00 440 4 550 $47.00 560 (b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? (P₂ PyPy Party lady la)-([ (c) How much money (in dollars) could Acme save if they were willing to drop the restriction about producing at least 400 units per month?

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 46P
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Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items. Demand Production Cost Production Capacity MIN: Subject to: Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how many of each appliance to manufacture during each of the next four months to meet the expected demand at the lowest possible total cost. (Let P, number of units to produce in monthi and I, inventory held at the end of month (.) Inventory Month 1 (a) Formulate an LP model for this problem to minimize total cost (in dollars). (Enter your answers for production as a comma- separated list of inequalities and/or equations.) Inventory Month 2 Inventory Month 3 Inventory Month 4 Production Month 1 Production Month 2 Month Production Month 3 1 2 410 590 $49.00 $45.00 510 510 Production Month 4 3 300 $46.00 440 4 550 $47.00 560 (b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? (c) How much money (in dollars) could Acme save if they were willing to drop the restriction about producing at least 400 units per month?
Transcribed Image Text:Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items. Demand Production Cost Production Capacity MIN: Subject to: Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how many of each appliance to manufacture during each of the next four months to meet the expected demand at the lowest possible total cost. (Let P, number of units to produce in monthi and I, inventory held at the end of month (.) Inventory Month 1 (a) Formulate an LP model for this problem to minimize total cost (in dollars). (Enter your answers for production as a comma- separated list of inequalities and/or equations.) Inventory Month 2 Inventory Month 3 Inventory Month 4 Production Month 1 Production Month 2 Month Production Month 3 1 2 410 590 $49.00 $45.00 510 510 Production Month 4 3 300 $46.00 440 4 550 $47.00 560 (b) Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? (c) How much money (in dollars) could Acme save if they were willing to drop the restriction about producing at least 400 units per month?
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