Linear programming questions

Practice questions covering linear programming from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Linear programming, each with its mark scheme and worked method. Reveal the answer when you have had a go.

D1-5.1 · Formulation of problems as linear programs including the meaning and use of slack, surplus and artificial variables.
Q1
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
1.
A bakery makes $x$ loaves and $y$ rolls each day. A loaf uses $500$ g of flour and $12$ minutes of oven time; a roll uses $80$ g of flour and $3$ minutes. There are $60$ kg of flour and $600$ minutes of oven time available, and at least $40$ rolls must be made. A loaf sells for $£3$ and a roll for $£0.60$ . Formulate the problem as a linear program.
(6)
(Total for Question 1 is 6 marks)
D1-5.1 · Formulation of problems as linear programs including the meaning and use of slack, surplus and artificial variables.
Q2
ORIGINAL
Years 1 and 2
Years 1 and 2: this holds AS subject content and content the exam board adds beyond it for the full A-level.
2.
Write the constraint $4x+3y\leqslant36$ as an equation using a slack variable, and state what the slack variable measures.
(2)
(Total for Question 2 is 2 marks)
D1-5.2 · Graphical solution of two variable problems using objective line and vertex methods including cases where integer solutions are required.
Q3
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
3.
Maximise $P=5x+4y$ subject to $2x+3y\leqslant24$ , $3x+y\leqslant21$ , $x\geqslant0$ and $y\geqslant0$ , using the vertex method. Give your answer exactly.
(6)
(Total for Question 3 is 6 marks)
D1-5.2 · Graphical solution of two variable problems using objective line and vertex methods including cases where integer solutions are required.
Q4
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
4.
The feasible region of a linear program has vertices $(0,0)$ , $(6,0)$ , $(4,5)$ and $(0,7)$ . Use the vertex method to maximise $P=3x+2y$ .
(3)
(Total for Question 4 is 3 marks)
D1-5.3 · The Simplex algorithm and tableau for maximising and minimising problems with ≤ constraints.
Q5
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
5.
Maximise $P=5x+4y$ subject to $2x+3y\leqslant24$ and $3x+y\leqslant21$ with $x$ , $y\geqslant0$ , using the simplex algorithm. Give the final tableau and state the values of $x$ , $y$ , $s_1$ , $s_2$ and $P$ .
(8)
(Total for Question 5 is 8 marks)
D1-5.4 · The two-stage Simplex and big-M methods for maximising and minimising problems which may include both ≤ and ≥ constraints.
Q6
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
6.
For the problem of maximising $P=3x+2y$ subject to $x+y\leqslant10$ and $x+2y\geqslant8$ , with $x$ , $y\geqslant0$ , write down the initial big-M tableau, showing how the artificial variable is removed from the objective row.
(6)
(Total for Question 6 is 6 marks)

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Printable question pack — D1-5 Linear programmingAll 40 questions across 4 specification points — 34 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

D1-5 Linear programming revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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