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) Write the inequalities which represent each of the following conditions:
(a(i)) There must be at least one single room.[1]
Verified working — step 1
"At least one" m…(a(ii)) There must be at least 10 rooms altogether.[1]
Verified working — step 1
The total number of rooms is x …(a(iii)) The total number of rooms should not exceed 15.[1]
Verified working — step 1
"Should not exceed 1…(a(iv)) The number of double rooms must be at least twice the number of single rooms.[1]
Verified working — step 1
"Doubles at least twice the …(a(v)) The number of double rooms should not be more than 12.[1]
Verified working — step 1
"Doubles not more than…(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 x = 1, x + y = 10, x + y = 15, y = 2x (through the origin) and y = …(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 each vertex: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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question