ECZ 2019 · GCE Paper 2 · Question 7 — Linear Programming
Answer the whole of this question on a sheet of graph paper. Mipando makes two types of chairs for sale; dining and garden. He intends to make at least 10 dining chairs and at least 20 garden chairs. He wants to make not more than 80 chairs altogether. The number of garden chairs must not be more than three times the number of dining chairs.
(a) Let x be the number of dining chairs and y the number of garden chairs. Write four inequalities to represent the information above.[4]
Verified working — step 1
Let x = dining chairs, y = garden chairs.(b) Using a scale of 2 cm to represent 10 chairs on each axis, draw x and y axes for 0 ≤ x ≤ 80 and 0 ≤ y ≤ 80 respectively and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Scale 2 cm to 10 chairs on each axis, 0 to 80 both ways.(c) Given that the profit on the sale of a dining chair is K80.00 and profit on a garden chair is K50.00, how many chairs of each type should Mipando make in order to maximize the profit?[2]
Verified working — step 1
Profit P = 80x + 50y, tested at each corner of the region.(d) What is this maximum profit?[2]
Verified working — step 1
Use the optimal point (60, 20) in P = 80x + 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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