ECZ 2010 · O-Level Paper 2 · Question 11 — Linear Programming

Mr. Simukadi intends to buy a total of 500 scratch cards from Unitel and Bitel. He decides to buy Bitel scratch cards which must be at least one third of Unitel scratch cards. He wants to buy at least 150 Bitel scratch cards and not more than 300 Unitel scratch cards. Let x be the number of Unitel scratch cards and y be the number of Bitel scratch cards.

(a) Write down four inequalities which satisfy the above conditions.[4]

Verified working — step 1

Let x = Unitel cards and y = Bitel cards.

(b) Show these inequalities on graph paper using 2 cm to represent 100 scratch cards on both axes.[4]

Verified working — step 1

Scale 2 cm to 100 cards on both axes.

(c) The dealer makes a profit of K500 on each Unitel scratch card and K150 on each Bitel scratch card sold.

(c(i)) Find the number of scratch cards of each type he must buy in order to maximize his profit.[2]

Verified working — step 1

Profit P = 500x + 150y, tested at each vertex.

(c(ii)) Calculate the maximum profit.[2]

Verified working — step 1

Use the optimal point (300, 200) in P = 500x + 150y.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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