Industrial Gases, Inc. (IGI) produces a variety of compressed and liquified gases for use in industrial processes. This problem concerns their liquid nitrogen business. IGI has three plants capable of producing liquid nitrogen, which we refer to simply as plant 1, plant 2, and plant 3:
| Plant | Employees | Age (Years) | Capacity (Canisters/Week) |
Unit
Production Cost ($/Canister) |
|---|---|---|---|---|
| 1 | 23 | 12 | 45 | $ 40 |
| 2 | 41 | 21 | 60 | $ 50 |
| 3 | 28 | 8 | 55 | $ 37 |
Five customers have ordered liquid nitrogen for the coming week:
| Customer | 1 | 2 | 3 | 4 | 5 |
| Canisters Ordered | 45 | 20 | 25 | 30 | 30 |
The per-canister shipping costs from plants to customers are as follows:
| Unit shipping costs to Customer | |||||
| 1 | 2 | 3 | 4 | 5 | |
| Plant 1 | $ 8 | $ 6 | $ 7 | $ 10 | $ 9 |
| Plant 2 | $ 9 | $ 12 | $ 5 | $ 13 | $ 7 |
| Plant 3 | $ 14 | $ 9 | $ 12 | $ 16 | $ 5 |
To meet this week's demand in the cheapest possible way, where should IGI produce liquid nitrogen, and how should it ship liquid nitrogen to its customers?