ECZ 2026 · GCE Paper 2 · Question 10 — Linear Programming
A man intends to make two types of bricks, type A and type B for sale. He intends to make at least 100 type A bricks and at least 50 type B bricks. He wants to make at most 600 bricks altogether. The number of type B bricks must not be more than two times the number of type A bricks.
(a) Let x be the number of type A bricks and y the number of type B bricks. Write four inequalities which satisfy the above conditions.[4]
Verified working — step 1
"At least 100 type A": x ≥ 100.(b) Using a scale of 2cm to represent 100 bricks on each axis, draw the x-axis for 0 ≤ x ≤ 700 and y-axis for 0 ≤ y ≤ 700 respectively and shade the unwanted region to show clearly the region in which the solution of the inequalities lie.[4]
Verified working — step 1
Boundary lines: x = 100 vertical; y = 50 horizontal; x + y = 600 through (600, 0) and (0, 600); y = 2x through (0, 0) and (300, 600).(c) Given that the profit on the sale of a type A brick is K10.00 and on a type B brick is K15.00, how many bricks of each type should he make to maximise profit?[2]
Verified working — step 1
Profit P = 10x + 15y is greatest at a vertex of the region:(d) Calculate 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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question