ECZ 2020 · GCE Paper 2 · Question 12 — Linear Programming
Answer the whole of this question on a sheet of graph paper. Menda intends to run a business of selling mineral water. He needs to order at least 10 small bottles and at most 60 large bottles of water. He decides to order at most 80 bottles of water altogether and the number of large bottles he orders should be at least twice that of small bottles.
(a) Given that x is the number of small bottles and y is the number of large bottles, 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 bottles 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 = 10, y = 60, x + y = 80 through (80, 0) and (0, 80), and y = …(c) The profit on the sale of each small bottle of mineral water is K1.50 while on each large bottle of mineral water profit is K2.50. How many bottles of each type can be bought to make maximum profit?[2]
Verified working — step 1
Profit P = 1.50x + 2.50y, tested at each vertex:(d) Hence, find this maximum profit.[2]
Verified working — step 1
P = 1.50(20) + 2.50(60) = …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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