ECZ 2017 · O-Level Paper 2 · Question 11 — Linear Programming
Himakwebo orders maize and groundnuts for sale. The order price of a bag of maize is K75.00 and that of a bag of groundnuts is K150.00. He is prepared to spend up to K7 500.00 altogether. He intends to order at least 5 bags of maize and at least 10 bags of groundnuts. He does not want to order more than 70 bags altogether. Let x and y be the number of bags of maize and groundnuts respectively.
(a) If x and y are the number of bags of maize and groundnuts respectively, write four inequalities which represent these conditions.[4]
Verified working — step 1
Cost: 75x + 150y <= 7500, which simplifies to x + 2y <= 100.(b) Using a scale of 2 cm to represent 10 bags on each axis, draw the x and y axes for 0 <= x <= 70 and 0 <= y <= 70 respectively and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Shade above x + 2y = 100, left of x = 5, below y = 10 and above x + y = …(c) Given that the profit on a bag of maize is K25.00 and on a bag of groundnuts is K50.00, how many bags of each type should he order to have maximum profit?[2]
Verified working — step 1
Profit P = 25x + 50y, tested at the vertices:(d) What is this estimate of the maximum profit?[2]
Verified working — step 1
P = 25(40) + 50(30) = 1000 + 1500 = …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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