The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1900 B...
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The Ace Manufacturing Company has orders for three similar products:
Product Order (Units) A 1900 B 550 C 1300 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 as follows:
Machine Capacity (Units) 1 1400 2 1500 3 1100 Product Machine A B C 1 $1.00 $1.20 $0.80 2 $1.30 $1.40 $1.40 3 $1.00 $1.00 $1.50 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If required, round your answers to one decimal place.
The linear programming formulation and optimal solution are shown.
Let x1A Units of product A on machine 1 x1B = Units of product B on machine 1 • • • x3C = Units of product C on machine 3 Min x1A + x1B + x1C + x2A + x2B + x2C + x3A + x3B + x3C s.t. x1A + x1B + x1C ≤ x2A + x2B + x2C ≤ x3A + x3B + x3C ≤ x1A + x2A + + x3A = x1B + x2B + x3B = x1C + x2C + x3C = xij ≥ 0 for all i, j Optimal Solution Units Cost 1-A $ 1-B $ 1-C 2-A 2-B $ 2-C $ 3-A 3-B 3-C $ Total $
Homework Answers
| Min | 1.x1A | + | 1.2 x1B | + | 0.8 x1C | + | 1.3 x2A | + | 1.4 x2B | + | 1.4 x2C | + | 1 x3A | + | 1 x3B | + | 1.5 x3C | ||
| s.t. | |||||||||||||||||||
| 1 x1A | + | 1 x1B | + | 1 x1C | ≤ | 1400 | |||||||||||||
| 1 x2A | + | 1 x2B | + | 1 x2C | ≤ | 1500 | |||||||||||||
| 1 x3A | + | 1 x3B | + | 1 x3C | ≤ | 1100 | |||||||||||||
| 1 x1A | + | 1 x2A | + | + | 1 x3A | = | 1900 | ||||||||||||
| 1 x1B | + | 1 x2B | + | 1 x3B | = | 550 | |||||||||||||
| 1 x1C | + | 1 x2C | + | 1 x3C | = 1300 |
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The Ace Manufacturing Company has orders for three similar
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