Given: You are a planning engineer for a metropolitan area. You want to minimize the cost of land filling the refuse produced by Cities A, B, C, and D under your jurisdiction. Three of the cities have landfills (G, H, and I), but their capacities do not match up with the amount of waste produced in each city. Each city produces the following amount of refuse: A – 100 tons/day, B – 50 tons/day, C – 60 tons/day, D – 40 tons/day.
The city landfills have the following capacities: G – 50 tons/day, H – 75 tons/day, I – 150 tons/day
The cost per ton for hauling and land filling are given in the following matrix:
| To Landfills G,H,I | ||||
| From Cities A,B,C,D | G | H | I | |
| A | 10 | 20 | 30 | |
| B | 18 | 12 | 16 | |
| C | 22 | 18 | 26 | |
| D | 28 | 20 | 8 | |
Required: Solve this as a linear programming problem to minimize the total cost of disposing of all trash.