0580/41 Oct/Nov 2024, Question 7: Graphing a Single Inequality

Part (a) · 2 marks

Use the inequalities to state the maximum number of scientific calculators and the maximum total number of calculators made daily.

1. 1x < 180, so fewer than 180 scientific calculators
2. 2x + y ≤ 240, so a maximum of 240 calculators

Answer180 and 240

Part (b) · 1 mark

Using costs $12 and $18 with a minimum daily spend of $2700, show that 2x + 3y ≥ 450.

1. 1Cost = 12x + 18y, and this is at least 2700
2. 212x + 18y ≥ 2700
3. 3Divide by 6: 2x + 3y ≥ 450

Answer12x + 18y ≥ 2700 and completion to 2x + 3y ≥ 450

Part (c) · 7 marks

Draw four lines for the given inequalities on the grid, shade unwanted regions, and label the feasible region R.

1. 1Draw x = 180 as a broken vertical line (strict inequality); shade x > 180
2. 2Draw y = 90 as a solid line; shade above it
3. 3Draw x + y = 240 through (0, 240) and (240, 0) as a solid line; shade above it
4. 4Draw 2x + 3y = 450 through (0, 150) and (225, 0) as a solid line; shade below it. Label the unshaded region R

AnswerCorrect region R indicated, with x = 180 broken line and y = 90, x + y = 240 and 2x + 3y = 450 solid ruled lines

Part (d) · 2 marks

For region R, with profits $10 per scientific and $30 per graphic calculator, calculate the greatest possible daily profit.

1. 1Profit = 10x + 30y; try the vertices of R
2. 2Best point: y = 90 and x + y = 240, so x = 150
3. 3Profit = 150 × 10 + 90 × 30 = 1500 + 2700 = $4200

Answer4200

More past-paper questions on graphing a single inequality

• 4MA1/2FR Jan 2022 Q24 · 5 marks
• 4MA1/2FR Jun 2020 Q24 · 3 marks