ECZ 2014 · O-Level Paper 2 · Question 11 — Linear Programming
Question from ECZ 2014 · O-Level Paper 2 · Question 11
(a) The graph below shows four inequalities that satisfy the intentions of a businessman to purchase two types of soft drinks, A and B.
(a(i)) Given that x represents the number of type A soft drinks and y the number of type B, write the four inequalities that represent the unshaded region R.[4]
Verified working — step 1
The y-axis is shaded on its left: x ≥ 0.(a(ii)) If the profit on type A soft drinks is K2.00 per bottle and profit on type B is K3.00 per bottle, find the number of each type of soft drinks he must buy in order to make maximum profit.[1]
Verified working — step 1
Profit P = 2x + 3y, tested at each vertex of R.(a(iii)) Find this maximum profit.[2]
Verified working — step 1
Use the optimal point (10, 15) in P = 2x + 3y.(b) Two pupils are to represent a school at a Human Rights Conference. If the two are chosen at random from a group of 8 girls and 6 boys, calculate the probability that the two pupils picked
(b(i)) are both girls,[2]
Verified working — step 1
Total ways to choose 2 from 14 = 91.(b(ii)) at least one is a boy.[3]
Verified working — step 1
"At least one boy" is the complement of "both girls".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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