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Year 11

Higher

Advanced problem solving with linear inequalities

I can use my knowledge of inequalities to solve problems.

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New

Year 11

Higher

Advanced problem solving with linear inequalities

I can use my knowledge of inequalities to solve problems.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

When handling a project, there are often constraints.
Constraints exist for a variety of reasons, such as cost or supply limitations.
Finding a set of possible solutions allows you to work within the constraints.

Keywords

Inequality - An inequality is used to show that one expression may not be equal to another.

Common misconception

We are only interested in points that are in the region satisfied by all inequalities.

With practical contexts, such as project management, it is useful to know when one constraint is not being met as it can suggest where additional resources (if available) should be allocated.

Consider having pupils investigate what additional capacity would mean by changing the constraints. What options are available if the constraints still existed but had less restrictive values? How does this affect profit?

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

$$5x+15y=1200$$ is an equation whereas $$5x+15y<1200$$ is an .

Correct Answer: inequality

Q2.

$$(5,2)$$ is the point of of these two linear equations.

Correct Answer: intersection

Q3.

A young person starts with $$£50$$ savings and then saves $$£15$$ per week. Which inequality represents the time when they will have more than $$£500$$ in savings?

$$50w+15\geq500$$

$$50w+15>500$$

$$50w+15<500$$

$$50+15w\geq500$$

Correct answer: $$50+15w>500$$

Q4.

Which of these values satisfy this inequality? $${8x+12y}\le{480}$$

Correct answer: $$(15,30)$$

Correct answer: $$(30,15)$$

Correct answer: $$(40,10)$$

$$(10,40)$$

$$(40,15)$$

Q5.

Which of these values satisfy both of these inequalities simultaneously? $$y>2x+3$$ and $$y<12$$

Correct answer: $$(2,8)$$

$$(8,2)$$

Correct answer: $$(3,10)$$

$$(3,9)$$

$$(2,12)$$

Q6.

Which of these values satisfy both of these inequalities simultaneously? $$y>2x+3$$ and $$y\le12-x$$

Correct answer: $$(0,12)$$

$$(10,2)$$

Correct answer: $$(2,10)$$

$$(3,9)$$

Correct answer: $$(1,6)$$

Exit quiz

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6 Questions

Q1.

These inequalities model a company's packaging and production constraints. The values $$(15,20)$$ satisfy both inequalities __________.

Correct answer: simultaneously

independently

individually

Q2.

These inequalities model a company's packaging and production constraints. Which of these points satisfies the production constraint but not the packaging constraint?

$$(5,40)$$

$$(40,40)$$

Correct answer: $$(40,5)$$

$$(5,5)$$

Q3.

These inequalities model a company's packaging and production constraints. Which of these points satisfy both the production and the packaging constraints?

$$(5,35)$$

Correct answer: $$(35,5)$$

$$(10,30)$$

Correct answer: $$(30,10)$$

$$(15,30)$$

Q4.

These inequalities model a company's packaging and production constraints. Which coordinate pair is the point where both production and packaging are optimised?

Correct Answer: (30,15), (30, 15)

Q5.

This model has three constraints. $$x$$ represents the number of standard games produced, $$y$$ the number of deluxe ones. What is the maximum number of games that can be made?

Correct Answer: 18, Eighteen, 18 games

Q6.

This model has three constraints. $$x =$$ standard games, making $$£4$$ profit. $$y =$$ deluxe games, making $$£9$$ profit. What is the maximum profit achievable? $$£$$

Correct Answer: 104, £104