You are a planning engineer for a metropolitan area. You want to minimize the cost of landfilling the refuse ...

3. You are a planning engineer for a metropolitan area. You want to minimize the cost of landfilling the refuse produced by Cities A, B, C and D under your jurisdiction. Three of the cities (A, B and D) also have landfills, 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 landfills have the following capacities:

A: 50 tons/day

B: 75 tons/day

D: 150 tons/day

The cost per ton for hauling and landfilling are given in the following matrix:

Cities

Landfills

A

B

D

A

10

20

30

B

18

12

16

C

22

18

26

D

28

20

8

Formulate this as a linear programming problem to minimize the total cost of disposing of all trash.