ECZ 2019 · O-Level Paper 2 · Question 9 — Linear Programming
Kuunika wishes to build a lodge with single and double rooms. He needs to decide the number of each room type he should build to maximize profit. Let x represent the number of single rooms and y the number of double rooms.
(a(i)) Write the inequality which represents the condition: there must be at least one single room.[1]
Verified working — step 1
"At least one" means one or more, so x > = …(a(ii)) Write the inequality which represents the condition: there must be at least 10 rooms altogether.[1]
Verified working — step 1
The total number of rooms is x…(a(iii)) Write the inequality which represents the condition: the total number of rooms should not exceed 15.[1]
Verified working — step 1
"Should not exceed 15" means at most 15, so x + y < = …(a(iv)) Write the inequality which represents the condition: the number of double rooms must be at least twice the number of single rooms.[1]
Verified working — step 1
Twice the number of single rooms is …(a(v)) Write the inequality which represents the condition: the number of double rooms should not be more than 12.[1]
Verified working — step 1
"Not more than 12" means at most 12, so y < = …(b) Using a scale of 2 cm to 5 units on both axes, draw x and y axes for 0 <= x <= 16 and 0 <= y <= 16 respectively and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[5]
Verified working — step 1
Draw each boundary line, then shade the side of each tha…(c) The rate for a single room is K600.00 and K900.00 for a double room. How many rooms of each type should Kuunika build to maximize the income?[2]
Verified working — step 1
Income I = 600x + 900y, tested at the vertices: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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