ECZ 2016 · GCE Paper 2 · Question 9 — Linear Programming
Question from ECZ 2016 · GCE Paper 2 · Question 9
(a) The region R in the diagram below shows the set of points (x, y) satisfying four inequalities representing the number of chairs (x) and tables (y) a carpenter made.
(a(i)) If two of the inequalities are y ≥ 20 and y ≥ 2x + 10, write the other two inequalities.[3]
Verified working — step 1
(Note: the paper prints y ≥ 2x + 10, but the shaded region R matches y ≤ 2x + 10 — a printing error; this solution uses y ≤ 2x + 10.)(a(ii)) The carpenter makes a profit of K100.00 on a chair and K60.00 on a table sold. Given that the carpenter sold all the chairs and tables he made, find the
(a(ii)(a)) values of x and y which would give him maximum profit,[2]
Verified working — step 1
Maximise P = 100x + 60y over the corners of R.(a(ii)(b)) maximum profit.[2]
Verified working — step 1
Use the optimal point (110, 40) in P = 100x + 60y.(b) A bag contains 3 black balls and 2 white balls. Two balls are taken from the bag at random, one after another, without replacement.
(b(i)) Draw a tree diagram to represent this information.[3]
Verified working — step 1
5 balls in total, drawn WITHOUT replacement, so 4 remain for the second draw.(b(ii)) Calculate the probability that the two balls taken at random are of the same colour.[2]
Verified working — step 1
Same colour = both black or both white.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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