ECZ 2017 · GCE Paper 2 · Question 11 — Linear Programming
Answer this question on a sheet of graph paper. Makwebo prepares two types of sausages, hungarian and beef, daily for sale. She prepares at least 40 hungarian and at least 10 beef sausages. She prepares not more than 160 sausages altogether. The number of beef sausages prepared are not more than the number of hungarian sausages.
(a) Given that x represents the number of hungarian sausages and y the number of beef sausages, write four inequalities which represent these conditions.[4]
Verified working — step 1
Let x = hungarian sausages, y = beef sausages.(b) Using a scale of 2 cm to represent 20 sausages on both axes, draw the x and y axes for 0 ≤ x ≤ 160 and 0 ≤ y ≤ 160 respectively and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Scale 2 cm to 20 sausages on both axes, 0 to 160 each way.(c) The profit on the sale of each hungarian sausage is K3.00 and on each beef sausage is K2.00. How many of each type of sausages are required to be prepared to make maximum profit?[2]
Verified working — step 1
Profit P = 3x + 2y, tested at each corner.(d) Calculate this maximum profit.[2]
Verified working — step 1
Use the optimal point (150, 10) in P = 3x + 2y.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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