ECZ 2020 · GCE Paper 2 · Question 12 — Linear Programming
Menda sells mineral water: at least 10 small bottles, at most 60 large bottles, at most 80 bottles altogether, and the number of large bottles at least twice the number of small bottles. x = small, y = large.
(a) Write four inequalities which represent these conditions.[4]
Verified working — step 1
Let x = number of small bottles, y = number of large bottles.(b) Using a scale of 2cm 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
Using a scale of 2 cm to 10 units on both axes, draw the x-axis from 0 to 80 and the y-axis from 0 to 80.(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 function: P = 1.50x + 2.50y(d) Hence, find this maximum profit.[2]
Verified working — step 1
Using the values from (c): x = 20, y = 60The 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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question