ElectroExpert makes three models of slip rings. The current order amount for each model is given in the table below. Making slip rings requires wiring and harnessing operations. Currently ElectroExpert only has 10,000 hours of wiring and 5,000 hours of harnessing available. Each model has different per-unit wiring and harnessing hour consumption as given in the table below. ElectroExpert can either make in house or buy from outside to fulfill the orders. The respective unit costs are also given in the table below. Model 1 Model 2 Model 3 # of slip rings ordered 3000 2000 1000 Hours of wiring per unit 2 1.5 3 Hours of harnessing per unit 1 2 1 Cost ($) per unit to make 50 80 130 cost($) per unit to buy 60 100 150 Two additional constraints: Of the total number of hours of harnessing required in the plan, no more than 50% should be used to wire Model 2. Of the total $ amount spent on Model 2 (i.e., the total cost of making and buying Model 2), no more than 60% should be spent on buying. The goal is to minimize the total cost while satisfying all the relevant constraints. Formulate this problem as a linear programming model. DO NOT SOLVE.
ElectroExpert makes three models of slip rings. The current order amount for each model is given in the table below. Making slip rings requires wiring and harnessing operations. Currently ElectroExpert only has 10,000 hours of wiring and 5,000 hours of harnessing available. Each model has different per-unit wiring and harnessing hour consumption as given in the table below. ElectroExpert can either make in house or buy from outside to fulfill the orders. The respective unit costs are also given in the table below. Model 1 Model 2 Model 3 # of slip rings ordered 3000 2000 1000 Hours of wiring per unit 2 1.5 3 Hours of harnessing per unit 1 2 1 Cost ($) per unit to make 50 80 130 cost($) per unit to buy 60 100 150 Two additional constraints: Of the total number of hours of harnessing required in the plan, no more than 50% should be used to wire Model 2. Of the total $ amount spent on Model 2 (i.e., the total cost of making and buying Model 2), no more than 60% should be spent on buying. The goal is to minimize the total cost while satisfying all the relevant constraints. Formulate this problem as a linear programming model. DO NOT SOLVE.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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ElectroExpert makes three models of slip rings. The current order amount for each model is given in the table below.
Making slip rings requires wiring and harnessing operations. Currently ElectroExpert only has 10,000 hours of wiring and 5,000 hours of harnessing available. Each model has different per-unit wiring and harnessing hour consumption as given in the table below.
ElectroExpert can either make in house or buy from outside to fulfill the orders. The respective unit costs are also given in the table below.
| Model 1 | Model 2 | Model 3 | |
| # of slip rings ordered | 3000 | 2000 | 1000 |
| Hours of wiring per unit | 2 | 1.5 | 3 |
| Hours of harnessing per unit | 1 | 2 | 1 |
| Cost ($) per unit to make | 50 | 80 | 130 |
| cost($) per unit to buy | 60 | 100 | 150 |
Two additional constraints:
- Of the total number of hours of harnessing required in the plan, no more than 50% should be used to wire Model 2.
- Of the total $ amount spent on Model 2 (i.e., the total cost of making and buying Model 2), no more than 60% should be spent on buying.
The goal is to minimize the total cost while satisfying all the relevant constraints.
Formulate this problem as a linear programming model. DO NOT SOLVE.
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