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Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, x,, be the number of units of product / produced by machine j, etc.)

Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, x,, be the number of units of product / produced by machine j, etc.)

Practical Management Science
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...
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The Ace Manufacturing Company has orders for three similar products. Product Min A s.t. B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A LB B Ic C Product 4 2 3 Orders (units) Machine 1 Capacity Product A Orders Machine 2 Capacity Product B Orders Machine 3 Capacity Product C Orders 1,800 X20 for all i, j. 700 1,100 Capacity (units) 1,400 (a) Develop the linear programming formulation of this problem. (Let x₁ be the number of units of product A produced by XA1 machine 1, x,, be the number of units of product i produced by machine j, etc.) 1,500 1,000 1 Machine $1.00 $1.30 $1.10 2 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 3 (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1 XA2 XA3 XB1' XB2' XB3 XC1 XC2¹ XC3) = Determine the cost (in dollars) of the production schedule. Total = $
Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products. Product Min A s.t. B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A LB B Ic C Product 4 2 3 Orders (units) Machine 1 Capacity Product A Orders Machine 2 Capacity Product B Orders Machine 3 Capacity Product C Orders 1,800 X20 for all i, j. 700 1,100 Capacity (units) 1,400 (a) Develop the linear programming formulation of this problem. (Let x₁ be the number of units of product A produced by XA1 machine 1, x,, be the number of units of product i produced by machine j, etc.) 1,500 1,000 1 Machine $1.00 $1.30 $1.10 2 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 3 (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1 XA2 XA3 XB1' XB2' XB3 XC1 XC2¹ XC3) = Determine the cost (in dollars) of the production schedule. Total = $
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