D1 June 2009 Q7

EdexcelOld spec14 marksLinear Programming

7. Rose makes hanging baskets which she sells at her local market. She makes two types, large and small.

Rose makes \(x\) large baskets and \(y\) small baskets.

Each large basket costs £7 to make and each small basket costs £5 to make. Rose has £350 she can spend on making the baskets.

(a) Write down an inequality, in terms of \(x\) and \(y\), to model this constraint. (2)

Two further constraints are

\[\begin{aligned} &y \leqslant 20 \text{ and}\\ &y \leqslant 4x.\end{aligned}\]
(b) Use these two constraints to write down statements that describe the numbers of large and small baskets that Rose can make. (2)
(c) On the grid provided, show these three constraints and \(x \geqslant 0\), \(y \geqslant 0\). Hence label the feasible region, R. (4)

Rose makes a profit of £2 on each large basket and £3 on each small basket. Rose wishes to maximise her profit, £\(P\).

(d) Write down the objective function. (1)
(e) Use your graph to determine the optimal numbers of large and small baskets Rose should make, and state the optimal profit. (5)
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