AS June 2025 Q4

EdexcelAS paperCurrent spec11 marksLinear Programming

4.

Figure 3: graph with x from 0 to 16 and y from 0 to 32; the line from (0, 20) to (16, 0) is drawn and the region above it is shaded
Figure 3

George is a baker who bakes \(x\) sponge cakes and \(y\) fruit cakes every day.

One of George’s constraints is shown on Figure 3.

(a) Write down this constraint as a simplified inequality with integer coefficients. (1)

Three further constraints are

  • George must bake at least four fruit cakes every day
  • for every two sponge cakes George bakes, he must bake at most three fruit cakes
  • George needs 200 g of butter for each sponge cake and 100 g for each fruit cake and has 2.8 kg of butter available each day
(b)
(i) Write down the three inequalities which model these constraints. Give your answers in simplified form with integer coefficients.
(ii) Add lines and shading to Diagram 1 in the answer book to represent these three constraints. Hence determine the feasible region and label it \(R\). (5)

[Diagram 1 in the answer book is a copy of Figure 3.]

George makes £8 profit from each sponge cake he sells and £5 profit from each fruit cake he sells. Given that he wishes to maximise his profit,

(c) use the vertex method to determine the number of sponge cakes and the number of fruit cakes George should bake each day. You must make your method and working clear. (5)
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