ECZ 2016 · O-Level Paper 2 · Question 11 — Linear Programming

A Health Lobby Group produced a guide to encourage healthy living among the local community. The group produced the guide in two formats: a short video and a printed book. The group needed to decide the number of each format to produce for sale to maximise profit. Let x represent the number of videos produced and y the number of printed books produced.

(a(i)(a)) Write the inequality which represents the condition: the total number of copies produced should not be more than 800.[1]

Verified working — step 1

The total number of copies is x + y, and it must not exceed 800, so x + y < = …

(a(i)(b)) Write the inequality which represents the condition: the number of video copies to be at least 100.[1]

Verified working — step 1

"At least 100" means 100 or more, so x > = …

(a(i)(c)) Write the inequality which represents the condition: the number of printed books to be at least 200.[1]

Verified working — step 1

"At least 200" means 200 or more, so y > = …

(a(ii)) Using a scale of 2 cm to represent 100 copies on both axes, draw the x and y axes for 0 <= x <= 800 and 0 <= y <= 800 respectively and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[4]

Verified working — step 1

Draw x = 100 (vertical), y = 200 (horizontal) and x + y = …

(a(iii)) The profit on the sale of each video copy is K15.00 while profit on each printed book is K8.00. How many of each type were produced to make maximum profit?[2]

Verified working — step 1

Profit P = 15x + 8y, tested at the vertices of the feasible region:

(b(i)) Maphone manufacturing company paid a total dividend of K12 600 000.00 at the end of 2015 on 600 shares. Calculate the dividend per share.[2]

Verified working — step 1

Dividend per share = 12 600 000600= …

(b(ii)) Magula owned 200 shares in the company. How much was paid out in dividends to her?[1]

Verified working — step 1

200 x K21 000 = …

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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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