ECZ 2025 · GCE Paper 2 · Question 12 — Linear Programming
A woman intends to order apples and oranges for sale. x = number of apples, y = number of oranges.
(a(i)) The total number of apples and oranges should not exceed 70. Write the inequality.[1]
Verified working — step 1
Total apples and oranges…(a(ii)) The number of oranges should not be more than twice that of apples. Write the inequality.[1]
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Oranges should not be more…(a(iii)) She has to order not more than 40 apples and at least 10 oranges. Write the inequalities.[2]
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Not more than 4…(b) Using a scale of 2cm 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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Draw x-axis and y-axis from 0 to 80 using a scale of 2cm to 10 units on both axes.(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 function: P = 2.50x + 1.50y(c(ii)) Calculate this maximum profit.[2]
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Using x = 40, y = 30 in P = 2.50x + 1.50y: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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