ECZ 2023 · O-Level Paper 2 · Question 9 — Linear Programming
A man intends to buy goats and cows for sale. He decides to buy not more than 50 goats and not more than 40 cows. He plans to buy at least 60 animals altogether.
(a) Given that x represents the number of goats and y the number of cows, write three inequalities which represent these conditions.[4]
Verified working — step 1
Not more than 50 goats: x <= 50.(b) Using a scale of 2 cm to represent 10 animals on each axis, draw the x and y axes for 0 <= x <= 80 and 0 <= y <= 80 respectively and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Draw x = 50, y = 40 and x + y = …(c) The profit on the sale of a goat is K100.00 and on a cow the profit is K800.00. How many animals of each type should he buy to make maximum profit?[2]
Verified working — step 1
Profit P = 100x + 800y, tested at the vertices:(d) What is the maximum profit?[2]
Verified working — step 1
P = 100(50) + 800(40) = 5000 + 32000 = …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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