ECZ 2021 · O-Level Paper 2 · Question 9 — Linear Programming
A traditional drinks dealer stocks two brands of drinks, brand A and brand B, both of which are produced in bottles of the same size. He wishes to order fresh supplies and finds that he has room for up to 900 bottles. He knows that brand A is more popular and so decides to order at least twice as many bottles of brand A as brand B. He wishes, however, to have at least 100 bottles of brand B and not more than 700 bottles of brand A. Let x be the number of bottles of brand A and y the number of bottles of brand B.
(a) Let x be the number of bottles of brand A and y the number of bottles of brand B. Write four inequalities to represent the information above.[4]
Verified working — step 1
Room for up to 900 bottles: x + y <= 900.(b) Using a scale of 2 cm to represent 100 bottles on each axis, draw x and y axes for 0 <= x <= 900 and 0 <= y <= 900 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 + y = 900 through (900, 0) and (0, 900), x = 2y through the origin and (900, 450), y = 100 and x = …(c(i)) Given that the profit on a bottle of brand A is K3.00 and on a bottle of brand B is K2.00, find the number of bottles of each brand that gives maximum profit.[2]
Verified working — step 1
Profit P = 3x + 2y, tested at the vertices:(c(ii)) Find the maximum profit.[2]
Verified working — step 1
P = 3(700) + 2(200) = 2100 + 400 = …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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