ECZ 2020 · O-Level Paper 2 · Question 12 — Linear Programming
A carpenter intends to manufacture at least 10 tables and at least 20 chairs. Each table requires 4 hours of assembling and 2 hours of varnishing. Each chair requires 3 hours of assembling and 1 hour of varnishing. There are 240 hours available for assembling and 100 hours for varnishing.
(a) Given that x represents the number of tables and y the number of chairs, write four inequalities which represent these conditions.[4]
Verified working — step 1
Translate each condition:(b) Using a scale of 2 cm to represent 10 pieces of furniture on each axis, draw the x and y axes for 0 ≤ x ≤ 70 and 0 ≤ y ≤ 100 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 = 10, y = 20, 4x + 3y = 240 through (60, 0) and (0, 80), and 2x + y = …(c) Each table sold yields a profit of K300.00 while each chair sold yields a profit of K250.00. Find the best combination of the number of tables and chairs to gain the maximum profit.[2]
Verified working — step 1
Profit P = 300x + 250y is maximised at a vertex.(d) Calculate this estimate of the maximum profit.[2]
Verified working — step 1
P = 300(10) + 250(66) = 3000 + 16500The 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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