ECZ 2023 · GCE Paper 2 · Question 9 — Linear Programming
A lady intends to bake two types of cakes, type A and type B, for sale. She intends to bake at least 30 cakes of type A and at least 20 cakes of type B. The number of cakes of type A must be equal to or more than the number of cakes of type B. The total number of cakes must not exceed 90. x = type A, y = type B.
(a) Write four inequalities to represent the information above.[4]
Verified working — step 1
Let x = number of type A cakes, y = number of type B cakes.(b) Using a scale of 2cm to represent 10 cakes on each axis, draw x and y axes for 0 ≤ x ≤ 90 and 0 ≤ y ≤ 90 respectively and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[5]
Verified working — step 1
Draw the x-axis (type A) and y-axis (type B), each from 0 to 90, using a scale of 2cm to 10 cakes.(c) The profit on the sale of a type A cake is K30.00 and the profit on a type B cake is K50.00. How many cakes of each type can be baked to make maximum profit?[2]
Verified working — step 1
Profit function: P = 30x + 50y.(d) Calculate the maximum profit.[1]
Verified working — step 1
Using the vertex (45,45):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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