ECZ 2021 · GCE Paper 2 · Question 10 — Linear Programming
A businessman orders two types of vehicles, sedans and vans, for sale. He orders at least 60 sedans and at least 20 vans. He orders not more than 180 vehicles altogether. The number of vans ordered is not more than the number of sedans. x = sedans, y = vans.
(a) Write four inequalities which satisfy the above conditions.[4]
Verified working — step 1
Let x = number of sedans, y = number of vans.(b) Using a scale of 2cm to represent 20 vehicles on each axis, draw x and y axes from 0 to 180 and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Using a scale of 2 cm : 20 vehicles on both axes, draw the x-axis (sedans) and y-axis (vans) from 0 to 180.(c) If the profit on the sale of a sedan is K10 000.00 and that on each van is K12 000.00, how many of each type should he order to make maximum profit?[2]
Verified working — step 1
The maximum profit occurs at one of the corner (vertex) points of the unshaded region found in (b):(d) Find this maximum profit.[2]
Verified working — step 1
From part (c), the maximum profit occurs at (x,y) = (90,90).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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