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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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PRODUCTION-MIX EXAMPLE SOLVE: Solve this LP problem as formulated. What is the solution?
Transcribed Image Text:PRODUCTION-MIX EXAMPLE SOLVE: Solve this LP problem as formulated. What is the solution?
PRODUCTION-MIX EXAMPLE Example: Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to acrospace firms that hold NASA contracts. Each of the products must pass through the following depart- ments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in this table: DEPARTMENT PRODUCT DRILLING INSPECTION UNIT PROFIT WIRING ASSEMBLY XJ201 .5 3. .5 XM897 1.5 4 1.0 $12 TR29 $15 1.5 1 .5 BR788 1.0 .5 $11 The production time available in each department each month and the minimum monthly production requirement to fulfill contracts are as follows: DEPARTMENT CAPACITY (HOURS) MINIMUM PRODUCTION LEVEL PRODUCT Wiring 1,500 XJ201 150 Drilling 2,350 XM897 100 Assembly 2,600 TR29 200 Inspection 1,200 BR788 400 Example: APPROACH ► Formulate this production-mix situation as an LP problem. The production manager first specifies production levels for each product for the coming month. He lets: X, = number of units of XJ201 produced X2 = number of units of XM897 produced X3 = number of units of TR29 produced X4 = number of units of BR788 produced SOLUTION The LP formulation is: Objective: Maximize profit = 9X1 + 12X, + 15X3 + 11X, subject to: .5X + 1.5X, + 1.5X3 + 1X4 s 1,500 hours of wiring available 3X1 + 1X2 + 2X3 + 3X4 s 2,350 hours of drilling available 2X, + 4X2 + 1X3 + 2X45 2,600 hours of assembly available .5X, + 1X + .5X3 + .5X4 s 1,200 hours of inspection X 2 150 units of XJ201 Xz z 100 units of XM897 X3 z 200 units of TR29 X4 z 400 units of BR788 X1, Xz. X3, Xạ z 0 INSIGHT There can be numerous constraints in an LP problem. The constraint right-hand sides may be in different units, but the objective function uses one common unit–dollars of profit, in this case. Because there are more than two decision variables, this problem is not solved graphically.
Transcribed Image Text:PRODUCTION-MIX EXAMPLE Example: Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to acrospace firms that hold NASA contracts. Each of the products must pass through the following depart- ments before they are shipped: wiring, drilling, assembly, and inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in this table: DEPARTMENT PRODUCT DRILLING INSPECTION UNIT PROFIT WIRING ASSEMBLY XJ201 .5 3. .5 XM897 1.5 4 1.0 $12 TR29 $15 1.5 1 .5 BR788 1.0 .5 $11 The production time available in each department each month and the minimum monthly production requirement to fulfill contracts are as follows: DEPARTMENT CAPACITY (HOURS) MINIMUM PRODUCTION LEVEL PRODUCT Wiring 1,500 XJ201 150 Drilling 2,350 XM897 100 Assembly 2,600 TR29 200 Inspection 1,200 BR788 400 Example: APPROACH ► Formulate this production-mix situation as an LP problem. The production manager first specifies production levels for each product for the coming month. He lets: X, = number of units of XJ201 produced X2 = number of units of XM897 produced X3 = number of units of TR29 produced X4 = number of units of BR788 produced SOLUTION The LP formulation is: Objective: Maximize profit = 9X1 + 12X, + 15X3 + 11X, subject to: .5X + 1.5X, + 1.5X3 + 1X4 s 1,500 hours of wiring available 3X1 + 1X2 + 2X3 + 3X4 s 2,350 hours of drilling available 2X, + 4X2 + 1X3 + 2X45 2,600 hours of assembly available .5X, + 1X + .5X3 + .5X4 s 1,200 hours of inspection X 2 150 units of XJ201 Xz z 100 units of XM897 X3 z 200 units of TR29 X4 z 400 units of BR788 X1, Xz. X3, Xạ z 0 INSIGHT There can be numerous constraints in an LP problem. The constraint right-hand sides may be in different units, but the objective function uses one common unit–dollars of profit, in this case. Because there are more than two decision variables, this problem is not solved graphically.
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