Linear Programming

Inequalities Level 1 Level 2 Level 3 Level 4 Level 5 Exam-Style Description Help More Graphs

A taxi company wishes to drive as many passengers as possible between Euston station and Wembley stadium. It has a fleet of two different types of vehicles: a car that can carry 5 passengers and a small van can carry 8 passengers.

The car uses £2 of fuel to make the journey and the van uses £3 of fuel to make the same journey.

The company has 10 drivers who could drive either cars or vans. The company policy limits spending to £25 on fuel per day while keeping at least 5 vehicles on the road.

This information is to be shown by shading unwanted regions on a graph. Let x be the number of cars and y the number of vans.

What inequality, in its simplest form, describes the region showing possible combinations due to the amount of money available?


CorrectWrong

What inequality, in its simplest form, describes the region showing possible combinations due to the number of drivers available?


CorrectWrong

What inequality describes the region showing there are enough vehicles on the road?


CorrectWrong

How many of each vehicle should the taxi company use if it wants to drive as many passengers as possible?

Maximum number of passengers: CorrectWrong

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Inequalities - A drag and drop inequality graph exercise

Level 1 - A question about building a new hotel with single and double rooms

Level 2 - A question about baking cakes with limited ingredients

Level 3 - A taxi company wants to transport the maximum number of passengers

Level 4 - A draft policy for selecting young people to attend the next World Scout Jamboree

Level 5 - A senior student does some jobs for neighbours to earn some pocket money

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

The Plot button colours in the unwanted region leaving the required region white.

A solid line means the required region does include the points on the line. A dotted line means the required region does not include the points on the line

The video above is from Andrew Chambers.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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