ECZ 2024 · GCE Paper 2 · Question 7 — Linear Programming
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. x = type A, y = type B.
(a) Write three inequalities which represent these conditions.[4]
Verified working — step 1
Cost per chair = K2000 for both types.(b) Using a scale of 2cm 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-axis (type A) and y-axis (type B), each from 0 to 70, using a scale of 2 cm to 10 chairs.(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
Identify the corner points (vertices) of the feasible region found in (b):(d) Calculate the maximum profit.[2]
Verified working — step 1
Using the point of maximum profit (60,10):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.
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