ECZ 2018 · GCE Paper 2 · Question 9 — Linear Programming
Answer the whole of this question on a sheet of graph paper. A tailor at a certain market intends to make dresses and suits for sale.
(a) Let x represent the number of dresses and y the number of suits. Write the inequalities which represent each of the conditions below.
(a(i)) The number of dresses should not exceed 50.[1]
Verified working — step 1
"Should not exceed 5…(a(ii)) The number of dresses should not be less than the number of suits.[1]
Verified working — step 1
"Dresses not less than suits" means dr…(a(iii)) The cost of making a dress is K140.00 and that of a suit is K210.00. The total cost should be at least K10 500.00.[2]
Verified working — step 1
Cost of x dresses = 140x, cost of y suits = …(b) Using a scale of 2 cm to represent 10 units on both axes, draw x and y axes for 0 ≤ x ≤ 60 and 0 ≤ y ≤ 80. Shade the unwanted region to indicate clearly the region where (x, y) must lie.[4]
Verified working — step 1
Scale 2 cm to 10 units, x from 0 to 60, y from 0 to 80.(c) The profit on a dress is K160.00 and on a suit it is K270.00.
(c(i)) Find the number of dresses and suits the tailor must make for maximum profit.[2]
Verified working — step 1
Profit P = 160x + 270y, tested at the feasible corners.(c(ii)) Calculate this maximum profit.[2]
Verified working — step 1
Use the optimal point (50, 50) in P = 160x + 270y.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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