- A glazing company runs a promotion for a special type of window. As a result of this the company receives orders for 30 of these windows from business \(B _ { 1 } , 18\) from business \(B _ { 2 }\) and 22 from business \(B _ { 3 }\). The company has stocks of 20 of these windows at factory \(F _ { 1 } , 35\) at factory \(F _ { 2 }\) and 15 at factory \(F _ { 3 }\). The table below shows the profit, in pounds, that the company will make for each window it sells according to which factory supplies each business.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | \(B _ { 1 }\) | \(B _ { 2 }\) | \(B _ { 3 }\) |
| \(F _ { 1 }\) | 20 | 14 | 17 |
| \(F _ { 2 }\) | 18 | 19 | 19 |
| \(F _ { 3 }\) | 15 | 17 | 23 |
The glazing company wishes to supply the windows so that the total profit is a maximum.
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 and state what each one represents.