2. A supplier has three warehouses, \(A , B\) and \(C\), at which there are 42,26 and 32 crates of a particular cereal respectively. Three supermarkets, \(D , E\) and \(F\), require 29, 47 and 24 crates of the cereal respectively.
The supplier wishes to minimise the cost in meeting the requirements of the supermarkets. The cost, in pounds, of supplying one crate of the cereal from each warehouse to each supermarket is given in the table below.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | \(D\) | \(E\) | \(F\) |
| \(A\) | 19 | 22 | 13 |
| \(B\) | 18 | 14 | 26 |
| \(C\) | 27 | 16 | 19 |
Formulate this information as a linear programming problem.
- State your decision variables.
- Write down the objective function in terms of your decision variables.
- Write down the constraints, explaining what each one represents.