ECZ 2013 · O-Level Paper 2 · Question 10 — Linear Programming
Question from ECZ 2013 · O-Level Paper 2 · Question 10
(a) A farmer wants to buy some hoes and shovels for use at his farm. He decides to buy at least 5 hoes and not more than 14 hoes and shovels altogether. The number of hoes should not be more than twice the number of shovels.
(a(i)) Taking x to represent the number of hoes and y the number of shovels, write three inequalities which satisfy the above conditions.[3]
Verified working — step 1
Let x = hoes and y = shovels.(a(ii)) The point (x, y) represents x hoes and y shovels. Using a scale of 1 cm to represent 1 unit on both axes, draw the x and y axes for -1 ≤ x ≤ 15 and -1 ≤ y ≤ 15 and shade the unwanted region to indicate clearly the region where (x, y) must lie.[3]
Verified working — step 1
Scale 1 cm to 1 unit on both axes, x and y from -1 to 15.(a(iii)) Find the largest number of shovels that can be bought.[1]
Verified working — step 1
To make y as large as possible, take x at its smallest allowed value, x = 5.(b) Kapofu bought three oranges and two apples which she put in a bag. Later on she picked one fruit at random from the bag and ate it. After some time she picked another fruit at random and ate it.
(b(i)) Construct a tree diagram to represent this information.[2]
Verified working — step 1
5 fruits at the first pick, and only 4 at the second because none is replaced.(b(ii)) Hence or otherwise, find the probability that the two fruits picked were of different types.[3]
Verified working — step 1
Different types = orange-then-apple or apple-then-orange.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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