ECZ 2011 · O-Level Paper 2 · Question 12 — Linear Programming
Question from ECZ 2011 · O-Level Paper 2 · Question 12
(a) A small scale farmer wishes to keep sheep and goats. Let x represent the number of sheep and y represent the number of goats.
(a(i)) Write the inequalities which represent each of the following conditions:
(a(i)(a)) The number of sheep should not be more than 4.[1]
Verified working — step 1
Let x be the number of sheep.(a(i)(b)) A goat feeds on 4 kg of food while a sheep feeds on 2 kg of food per day. The total amount of food should be at least 8 kg per day.[2]
Verified working — step 1
Sheep eat 2 kg each and goats 4 kg each, so total food = 2x + 4y kg.(a(i)(c)) The number of sheep should be more than the number of goats.[1]
Verified working — step 1
"More than" is a strict ineq…(a(ii)) Using a scale of 2 cm to represent 1 unit on both axes, draw the x and y axes for 0 ≤ x ≤ 5 and 0 ≤ y ≤ 5 and shade the unwanted region to indicate clearly the region where the solution of the inequalities lies.[3]
Verified working — step 1
Scale 2 cm to 1 unit on both axes, 0 to 5 each way.(b) In a certain month, a survey was conducted on 250 High School pupils to find out the number that bought oranges (O), mangoes (M) and lemons (L). Their responses were as shown in the Venn diagram below.
(b(i)) Find the value of x.[2]
Verified working — step 1
All the Venn regions add to 250 pupils.(b(ii)) How many pupils bought Mangoes and Lemons but not Oranges?[2]
Verified working — step 1
Mangoes and Lemons but not Oranges is the M-and-L overlap outside O.(b(iii)) How many pupils bought one type of fruit only?[1]
Verified working — step 1
One type only = Oranges only + Mangoes only + Lemons only.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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