# Linear Programming

##### InequalitiesLevel 1Level 2Level 3Level 4Level 5Exam-StyleDescriptionHelpMore Graphs

Ben is in Year 13 at Doworkwell High School. Some days after school and at weekends Ben does some jobs for neighbours in return for some pocket money. Each month he keeps a record of the number of hours he spends gardening (x) and washing cars (y) because his mother has told him she does not want him to work more than 25 hours in a month doing these jobs.

Ben can usually choose which jobs he does and when he will do them during the month. He is however committed to do at least 7 hours gardening and 10 hours car washing for neighbours who are related to him.

In preparation for his forthcoming Maths exam, Ben’s uncle has asked him to figure out the number of different ways his time (in whole hours) can be split between gardening and car washing if the latter is less than 5 hours more than the former.

 What inequality will describe the region showing that the number of hours spent car washing is less than 5 hours more than the number of hours gardening? What inequality will describe the region showing that no more than 25 hours can be worked in a month? What inequality will describe the region related to the fact that he is already committed to 7 hours gardening? What inequality will describe the region related to the fact that he is already committed to 10 hours car washing?

What is the number of different ways his time (in whole hours) can be split between gardening and car washing?

Number of possibilities:

If Ben gets paid £6 an hour for gardening and £8 an hour car washing which of the combinations mentioned in the previous question would be most profitable for Ben?

Hours spent gardening:   Hours spent car washing:

Check

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## Description of Levels

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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

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## Help

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

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