ECZ 2018 · GCE Paper 2 · Question 9 — Linear Programming

A tailor intends to make dresses and suits for sale. x = number of dresses, y = number of suits.

(a(i)) The number of dresses should not exceed 50. Write the inequality.[1]

Verified working — step 1

Since the number of dresses (x)…

(a(ii)) The number of dresses should not be less than the number of suits. Write the inequality.[1]

Verified working — step 1

The number of dresses must not be less than the number of…

(a(iii)) The cost of a dress is K140.00 and of a suit K210.00; total cost should be at least K10 500.00. Write the inequality.[2]

Verified working — step 1

Cost of x dresses = 140x, cost of y suits = …

(b) Using 2cm to 10 units on both axes (0 ≤ x ≤ 60, 0 ≤ y ≤ 80), shade the unwanted region.[4]

Verified working — step 1

Draw axes with 2cm representing 10 units, x from 0 to 60 and y from 0 to 80.

(c(i)) Profit is K160.00 per dress and K270.00 per suit. Find the number of dresses and suits for maximum profit.[2]

Verified working — step 1

The feasible region has corner points found from the boundary lines. Testing the vertices of the feasible region in the profit function P = 160x + 270y:

(c(ii)) Calculate this maximum profit.[2]

Verified working — step 1

Maximum profit = 160x + 270y at (x,y) = (50,50):

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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