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
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.
| Min | fill in the blank 1x1A | + | fill in the blank 2x1B | + | fill in the blank 3x1C | + | fill in the blank 4x2A | + | fill in the blank 5x2B | + | fill in the blank 6x2C | + | fill in the blank 7x3A | + | fill in the blank 8x3B | + | fill in the blank 9x3C | ||
| s.t. | |||||||||||||||||||
| fill in the blank 10x1A | + | fill in the blank 11x1B | + | fill in the blank 12x1C | ≤ | fill in the blank 13 | |||||||||||||
| fill in the blank 14x2A | + | fill in the blank 15x2B | + | fill in the blank 16x2C | ≤ | fill in the blank 17 | |||||||||||||
| fill in the blank 18x3A | + | fill in the blank 19x3B | + | fill in the blank 20x3C | ≤ | fill in the blank 21 | |||||||||||||
| fill in the blank 22x1A | + | fill in the blank 23x2A | + | + | fill in the blank 24x3A | = | fill in the blank 25 | ||||||||||||
| fill in the blank 26x1B | + | fill in the blank 27x2B | + | fill in the blank 28x3B | = | fill in the blank 29 | |||||||||||||
| fill in the blank 30x1C | + | fill in the blank 31x2C | + | fill in the blank 32x3C | = | fill in the blank 33 | |||||||||||||
| xij ≥ 0 for all i, j |
If required, round your answers to the nearest whole number.
| 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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