ECZ 2021 · GCE Paper 2 · Question 10 — Linear Programming
Answer the whole of this question on a sheet of graph paper. A businessman orders two types of vehicles namely; sedans and vans for sale. He orders at least 60 sedans and at least 20 vans. He orders not more than 180 vehicles altogether. He makes sure that the number of vans ordered are not more than the number of sedans ordered.
(a) Given that x represents the number of sedans and y represents the number of vans, write four inequalities which satisfy the above conditions.[4]
Verified working — step 1
Translate each condition:(b) Using a scale of 2 cm 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
Draw x = 60, y = 20, x + y = 180 through (180, 0) and (0, 180), and y = …(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
Profit P = 10000x + 12000y, tested at each vertex:(d) Find this maximum profit.[2]
Verified working — step 1
P = 10000(90) + 12000(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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