ECZ 2017 · GCE Paper 2 · Question 11 — Linear Programming

Makwebo prepares two types of sausages, hungarian and beef, daily for sale: at least 40 hungarian, at least 10 beef, not more than 160 sausages altogether, and beef not more than hungarian. x = hungarian, y = beef.

(a) Write four inequalities which represent these conditions.[4]

Verified working — step 1

Let x = number of hungarian sausages, y = number of beef sausages.

(b) Using 2cm to 20 sausages on both axes, draw the axes and shade the unwanted region.[4]

Verified working — step 1

Using scale 2cm to 20 sausages on both axes, draw the x-axis (hungarian) from 0 to 160 and y-axis (beef) from 0 to 160.

(c) Profit is K3.00 per hungarian and K2.00 per beef sausage. How many of each type should be prepared for maximum profit?[2]

Verified working — step 1

The feasible region has corner points: (40,10), (150,10), (80,80), (40,40).

(d) Calculate this maximum profit.[2]

Verified working — step 1

Using x = 150, y = 10 in P = 3x + 2y:

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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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