Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of product j on machine i.
Problem 6-09 (Algorithmic)
The Ace Manufacturing Company has orders for three similar products:
| Product | Order (Units) |
| A | 1750 |
| B | 500 |
| C | 1100 |
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 | 1550 |
| 2 | 1450 |
| 3 | 1150 |
| Product | |||
| Machine | A | B | C |
| 1 | $0.80 | $1.30 | $0.70 |
| 2 | $1.40 | $1.30 | $1.50 |
| 3 | $0.80 | $0.80 | $1.20 |
Use the transportation model to develop the minimum cost production
The linear programming formulation and optimal solution are shown.
Let xij = Units of product j on machine i.
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| Optimal Solution | Units | Cost |
|---|---|---|
| 1-A | fill in the blank 34 | $ fill in the blank 35 |
| 1-B | fill in the blank 36 | $ fill in the blank 37 |
| 1-C | fill in the blank 38 | $ fill in the blank 39 |
| 2-A | fill in the blank 40 | $ fill in the blank 41 |
| 2-B | fill in the blank 42 | $ fill in the blank 43 |
| 2-C | fill in the blank 44 | $ fill in the blank 45 |
| 3-A | fill in the blank 46 | $ fill in the blank 47 |
| 3-B | fill in the blank 48 | $ fill in the blank 49 |
| 3-C | fill in the blank 50 | $ fill in the blank 51 |
| Total $ fill in the blank 52 |
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