## Exam-Style Question on Linear Programming## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 335. This question is similar to one that appeared on a IGCSE Extended paper in 2010. The use of a calculator is allowed.

A large car park has an area of 1400m^{2} with space for \(x\) cars and \(y\) vans. Each car requires 14m^{2} of space and each van requires 35m^{2} of space.

(a) Show that \(2x+5y \le 200\)

(b) There must also be space for

(i) at least 50 vehicles,

(ii) at least 20 vans.

Write down two more inequalities to show this information.

(c) On the grid, show the three inequalities by drawing the three lines and shading the **unwanted** regions.

(d) Use your graph to find the largest possible number of vans.

(e) The company charges £6 for parking each car and £10 for parking each van. Find the number of cars and the number of vans which give the owners of the car park the greatest possible income and calculate this income.

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