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 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.
(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.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercises called Linear Programming.
©1997 - 2019 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/