ECZ 2018 · O-Level Paper 2 · Question 11 — Linear Programming
A hired bus is used to take learners and teachers on a trip. The number of learners and teachers must not be more than 60. There must be at least 35 people on the trip. There must be at least 6 teachers on the trip. The number of teachers on the trip should not be more than 14. Let x be the number of learners and y the number of teachers.
(a) Write four inequalities which represent the information above.[4]
Verified working — step 1
Let x = learners, y = teachers.(b) Using a scale of 2 cm to represent 10 units on both axes, draw the x and y axes for 0 ≤ x ≤ 70 and 0 ≤ y ≤ 70 respectively and shade the unwanted region to indicate clearly the region where the solution of the inequalities lie.[4]
Verified working — step 1
Scale 2 cm to 10 units on both axes, 0 to 70 each way.(c(i)) If the group has 25 learners, what is the minimum number of teachers that must accompany them?[1]
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Substitute x = 25 into x + y ≥ 35.(c(ii)) If 8 teachers go on this trip, what is the maximum number of learners that can be accommodated on the bus?[1]
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Substitute y = 8 into x + y ≤ 60.(d) If T is the amount in Kwacha paid by the whole group, what is the cost per learner if T = 30x + 50y?[2]
Verified working — step 1
In T = …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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