ECZ 2023 · GCE Paper 2 · Question 9 — Linear Programming
Answer the whole of this question on a sheet of graph paper. 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.
(a) Taking x to represent the number of cakes of type A and y to represent the number of type B cakes, write four inequalities to represent the information above.[4]
Verified working — step 1
Translate each condition:(b) Using a scale of 2 cm 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 x = 30, y = 20, x = y (through the origin at 45°), and x + y = 90 through (90, 0) and (0, 90).(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 P = 30x + 50y, tested at each vertex:(d) Calculate the maximum profit.[1]
Verified working — step 1
Substitute the winning vertex: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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