ECZ 2019 · GCE Paper 2 · Question 7 — Linear Programming

Mipando makes dining and garden chairs: at least 10 dining, at least 20 garden, not more than 80 altogether, and garden chairs not more than three times dining chairs. x = dining, y = garden.

(a) Write four inequalities to represent the information.[4]

Verified working — step 1

Let x = number of dining chairs, y = number of garden chairs.

(b) Using 2cm to 10 chairs on each axis (0 ≤ x ≤ 80, 0 ≤ y ≤ 80), shade the unwanted region.[4]

Verified working — step 1

Draw axes with 2 cm representing 10 chairs on both x (dining) and y (garden), covering 0 ≤ x ≤ 80 and 0 ≤ y ≤ 80.

(c) Profit is K80.00 per dining chair and K50.00 per garden chair. How many chairs of each type should Mipando make to maximize profit?[2]

Verified working — step 1

The feasible region is bounded by the corners:

(d) What is this maximum profit?[2]

Verified working — step 1

Using the optimal point (x,y) = (60,20):

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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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