ECZ 2025 · GCE Paper 2 · Question 12 — Linear Programming
A woman intends to order apples and oranges for sale.
(a) Let x represent the number of apples and y the number of oranges. Write the inequalities which represent each of the conditions described below.
(a(i)) The total number of apples and oranges should not exceed 70.[1]
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x apples and y oranges t…(a(ii)) The number of oranges should not be more than twice that of apples.[1]
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"Oranges not more than twice…(a(iii)) She has to order not more than 40 apples and at least 10 oranges.[2]
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"Not more than 40 apples": x < = …(b) Using a scale of 2 cm to represent 10 units on both axes, draw x and y axes from 0 to 80 and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[4]
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Boundary lines: x + y = 70 through (70, 0) and (0, 70); y = 2x through (0, 0) and (40, 80); x = 40 vertical; y = 10 horizontal.(c(i)) The profit on an apple is K2.50 and on an orange it is K1.50. Find the number of apples and oranges she should order for her to make maximum profit.[2]
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Profit P = 2.50x + 1.50y is maximised at a vertex of the feasible region.(c(ii)) Calculate this maximum profit.[2]
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Substitute the winning vertex into the profit expression: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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