ECZ 2024 · O-Level Paper 2 · Question 9 — Linear Programming
A businessman intends to make two types of products, A and B for sale. The cost of making product A is K60.00 and the cost of making product B is K30.00. The businessman has K3 000.00 to spend on the products. He decides to produce at least 20 of product A and at least 10 of product B.
(a) Let x be the number of product A and y be the number of product B. Write three inequalities which represent these conditions.[4]
Verified working — step 1
Cost: 60x + 30y ≤ 3000 — divide through by 30: 2x + y ≤ 100.(b) Using a scale of 2 cm to represent 10 units on each axis, draw the x-axis for 0 ≤ x ≤ 60 and y-axis for 0 ≤ y ≤ 100 respectively and shade the unwanted region to show clearly the region in which the solution of the inequalities lie.[4]
Verified working — step 1
Draw 2x + y = 100 through (50, 0) and (0, 100); x = 20 vertical; y = 10 horizontal.(c) The profit on the sale of product A is K80.00 and profit on the sale of product B is K50.00. How many products of each type can he make to maximise profit?[2]
Verified working — step 1
Profit P = 80x + 50y, tested at each vertex of the region:(d) Calculate the maximum profit.[2]
Verified working — step 1
P = 80(20) + 50(60) = …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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