ECZ 2016 · GCE Paper 2 · Question 9 — Linear Programming

Region R shows four inequalities for chairs (x) and tables (y); two are y ≥ 20 and y ≥ 2x + 10. Bag of 3 black and 2 white balls, two taken without replacement. [Note: the exam paper prints "y ≥ 2x + 10", but the shaded region R shown corresponds to "y ≤ 2x + 10" — treat the printed ≥ as a printing error and use y ≤ 2x + 10.]

(a(i)) If two 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 corresponds to 'y ≤ 2x + 10' (a printing error) — this solution uses y ≤ 2x + 10.

(a(ii)(a)) Profit K100chair, K60table. Find values of x and y giving maximum profit.[2]

Verified working — step 1

Maximise P = 100x + 60y over the corners of R.

(a(ii)(b)) Find the maximum profit.[2]

Verified working — step 1

Using x = 110, y = …

(b(i)) Bag of 3 black and 2 white balls, two taken without replacement. Draw a tree diagram.[3]

Verified working — step 1

Bag: 3 Black, 2 White, 5 total, drawn without replacement.

(b(ii)) Calculate the probability that the two balls are the same colour.[2]

Verified working — step 1

P(same colour) = …

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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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