ECZ 2025 · O-Level Paper 2 · Question 7 — Linear Programming
A man wishes to bake two types of scones, type P and type Q for sale. He must bake at least 10 scones of type P and at least 20 scones of type Q. The number of scones of type Q must not exceed twice the number of scones of type P. He intends to bake not more than 60 scones altogether.
(a) Given that x represents the number of scones of type P and y represents the number of scones of type Q, write four inequalities which satisfy the conditions above.[4]
Verified working — step 1
Translate each condition, keeping the direction of the phrase:(b) Using a scale of 2 cm to represent 10 units on each axis, draw x and y axes for 0 ≤ x ≤ 60 and 0 ≤ y ≤ 60 respectively and shade the unwanted region to show clearly where the solution of the inequalities lie.[4]
Verified working — step 1
Draw the four boundary lines: x = 10 (vertical), y = 20 (horizontal), y = 2x through (0, 0) and (30, 60), and x + y = 60 through (60, 0) and (0, 60).(c) If the profit on the sale of type P scones is K15.00 and profit on type Q is K20.00, find the number of each type of scones he should bake in order to make maximum profit.[2]
Verified working — step 1
The maximum of P = 15x + 20y occurs at a vertex of the feasible region, so test each vertex:(d) Calculate this estimate of the maximum profit.[2]
Verified working — step 1
Substitute the winning vertex into the profit expression:The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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