ECZ 2024 · GCE Paper 2 · Question 7 — Linear Programming
Answer the whole of this question on a sheet of graph paper. Mapulanga's carpentry shop makes two types of chairs, type A and type B for sale. The cost of making one chair of each type is K2 000.00. The shop has K140 000.00 available for making chairs. The number of chairs of type A must be at least 20 while that of type B must be at least 10.
(a) If x is the number of chairs of type A and y the number of chairs of type B, write three inequalities which represent these conditions.[4]
Verified working — step 1
Both chair types cost K2 000, so the budget line is 2000x + 2000y ≤ 140000.(b) Using a scale of 2 cm to represent 10 chairs on each axis, draw x and y axes for 0 ≤ x ≤ 70 and 0 ≤ y ≤ 70 respectively and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Draw x + y = 70 through (70, 0) and (0, 70); x = 20 vertical; y = 10 horizontal.(c) Given that the profit on a type A chair is K60.00 and on a type B is K30.00, how many chairs of each type should be made for maximum profit?[2]
Verified working — step 1
Profit P = 60x + 30y is maximised at a vertex of the region:(d) Calculate the maximum profit.[2]
Verified working — step 1
P = 60(60) + 30(10) = …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