ECZ 2015 · GCE Paper 2 · Question 11 — Linear Programming

Answer the whole of this question on graph paper.

(a) Mrs Kawena bakes two types of cakes for sale; type A and type B.

(a(i)) To satisfy her regular customers daily, she must bake; (a) at least 10 cakes of type A, (b) at least 20 cakes of type B. Taking x to represent the number of cakes of type A and y to represent cakes of type B, write two inequalities which satisfy the above conditions.[2]

Verified working — step 1

Let x be cakes of type A and y cakes of type B.

(a(ii)) To avoid wastage, the total number of cakes she should bake per day must not exceed 70. Write another inequality which satisfies this condition.[1]

Verified working — step 1

The total number of cakes is x + y.

(a(iii)) The point (x, y) represents x cakes of type A and y cakes of type B. Using a scale of 2 cm to represent 10 cakes on each axis, draw x and y axes for 0 ≤ x ≤ 80 and 0 ≤ y ≤ 80. Present the three inequalities above on your graph, and shade the unwanted region to indicate clearly the region where (x, y) must lie.[4]

Verified working — step 1

Scale 2 cm to 10 cakes on each axis, 0 to 80 both ways.

(b) Factorise completely 2x2 - 3x + 2cx - 3c.[2]

Verified working — step 1

Group the terms in pairs.

(c) Evaluate 2.04√0.25 + 1.5.[3]

Verified working — step 1

Work the denominator first.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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