ECZ 2022 · GCE Paper 2 · Question 7 — Linear Programming
Mapulanga plans to buy planks of type A and type B for sale at his hardware shop. He has to buy up to 80 planks altogether. The number of type B planks should not be more than 3 times that of type A. He decides to buy at least 10 planks of type A and at least 20 planks of type B. x = type A, y = type B.
(a) Write four inequalities which represent the above conditions.[4]
Verified working — step 1
Let x = number of type A planks, y = number of type B planks.(b) Using a scale of 2cm to represent 10 units on both axes from 0 to 80, shade the unwanted region to indicate clearly the region where (x, y) must lie.[4]
Verified working — step 1
Draw axes with x (type A) from 0 to 80 and y (type B) from 0 to 80, using 2 cm = 10 units.(c(i)) The profit on each type A plank is K30.00 and on each type B plank is K20.00. Find the number of each type that he can buy to make maximum profit.[2]
Verified working — step 1
The feasible region is a quadrilateral with corner points (vertices) found by solving pairs of boundary equations:(c(ii)) Calculate this maximum profit.[2]
Verified working — step 1
Using the optimal point (60, 20):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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