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0580/42 May/Jun 2024, Question 8: Finding Regions from Multiple Inequalities

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Given constraints on numbers of small and large cakes decorated daily, write the remaining inequalities, graph and shade the feasible region R, then find the maximum daily earnings using $8 per small cake and $12 per large cake.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Write the other three inequalities in x and y describing the limits on large cakes, the comparison between small and large cakes, and the total number of cakes.

  1. 1Less than 10 large cakes: y < 10
  2. 2More small than large: y < x
  3. 3Total not more than 24: x + y ≤ 24

Answery < 10, y < x, x + y ≤ 24

Part (b) · 6 marks

Draw four straight lines on the grid, shade the unwanted regions, and label the feasible region R satisfying all four inequalities.

  1. 1Draw x = 16 (solid), y = 10 (broken), y = x (broken), x + y = 24 (solid through (0, 24) and (24, 0))
  2. 2Shade x > 16, y > 10 side, above y = x and above x + y = 24
  3. 3Label the unshaded region R

AnswerCorrect lines and region R indicated

Part (c) · 2 marks

Using region R and earnings of $8 per small cake and $12 per large cake, find the largest possible daily earnings.

  1. 1Try integer points in R near the corner of y = 10 and x + y = 24
  2. 2y = 9, x = 15: 8 × 15 + 12 × 9 = 120 + 108 = 228
  3. 3y = 8, x = 16: 128 + 96 = 224 (smaller)
  4. 4Largest amount = $228

Answer228

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 8.
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