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Exam-Style Question on Linear Programming

A mathematics exam-style question with a worked solution that can be revealed gradually

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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 1400m2 with space for \(x\) cars and \(y\) vans. Each car requires 14m2 of space and each van requires 35m2 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.

Graph Paper

(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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If you need more practice try the self-checking interactive exercises called Linear Programming.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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