ECZ 2022 · O-Level Paper 2 · Question 7 — Linear Programming
A businessman intends to sell two types of markers, permanent and dry erase. He decides that there should be at least 20 permanent markers and at least 10 dry erase markers. In order to make his business stable, he decides to order not more than 70 markers altogether. The order price of a permanent marker is K15.00 and that of a dry erase marker is K20.00. He is prepared to spend not more than K1 200.00 altogether.
(a) Let x represent the number of permanent markers and y the number of dry erase markers. Write four inequalities which satisfy the above conditions.[5]
Verified working — step 1
At least 20 permanent markers: x >= 20.(b) Using a scale of 2 cm to represent 10 markers on each axis, draw x and y axes for 0 <= x <= 80 and 0 <= y <= 80 respectively and shade the unwanted region to show clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Draw x = 20, y = 10, x + y = 70 through (70, 0) and (0, 70), and 3x + 4y = …(c(i)) The profit on the sale of a permanent marker is K25.00 and on each dry erase marker the profit is K30.00. How many markers of each type should be ordered to make maximum profit?[2]
Verified working — step 1
Profit P = 25x + 30y, tested at the vertices:(c(ii)) Find the maximum profit.[1]
Verified working — step 1
P = 25(40) + 30(30) = 1000 + 900 = …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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