D1 January 2011 Q6

EdexcelOld spec11 marksLinear Programming

6.

Figure 6: axes x from 0 to 80 and y from 0 to 60; line from (0, 15) to (80, 55) with region above shaded; line from (0, 0) to (80, 20) with region below shaded
Figure 6

The graph in Figure 6 is being used to solve a linear programming problem.
Two of the constraints have been drawn on the graph and the rejected regions shaded out.

(a) Write down the constraints shown on the graph. (4)

Two further constraints are

\[\begin{aligned}x + y &\geqslant 30\\ \text{and}\quad 5x + 8y &\leqslant 400\end{aligned}\]
(b) Add two lines and shading to Graph 1 in your answer book to represent these constraints. Hence determine the feasible region and label it R. (4)

The objective is to

\[\text{minimise }\ 15x + 10y\]
(c) Draw a profit line on Graph 1 and use it to find the optimal solution. You must label your profit line clearly. (3)
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