ECZ 2022 · GCE Paper 2 · Question 7 — Linear Programming
Answer the whole of this question on a sheet of graph paper. 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.
(a) Given that x represents the number of planks of type A and y the number of type B, write four inequalities which represent the above conditions.[4]
Verified working — step 1
Translate each condition:(b) Using a scale of 2 cm 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 x + y = 80 through (80, 0) and (0, 80); y = 3x through (0, 0) and (20, 60); x = 10 vertical; y = …(c) The profit on each of type A plank is K30.00 and on each of type B plank profit is K20.00.
(c(i)) Find the number of each type that he can buy to make maximum profit.[2]
Verified working — step 1
Profit P = 30x + 20y, tested at each vertex:(c(ii)) Calculate this maximum profit.[2]
Verified working — step 1
P = 30(60) + 20(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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