ECZ 2018 · GCE Paper 1 — Linear Programming
In the diagram, R is the unshaded region bounded by three lines: the line through (0, 0) and (5, 5); the line through (0, 2) and (8, 0); and the line through (5, 5) and (8, 0). Write three inequalities which describe the region R.
- A. y ≤ x, y ≥ −¼x + 2, y ≤ −⁵⁄₃x + ⁴⁰⁄₃
- B. y ≥ x, y ≤ −¼x + 2, y ≥ −⁵⁄₃x + ⁴⁰⁄₃
- C. y ≤ x, y ≥ −¼x + 2, y ≤ −⅓x + 8
- D. y ≤ x, y ≤ −¼x + 2, y ≤ −⁵⁄₃x + ⁴⁰⁄₃
Verified working — step 1
Find each boundary line, then test which side R lies on. Line 1: through (0,0) and (5,5) is y = x; R is below it, so y ≤ x. Line 2: through (0,2) and (8,0) is y = −¼x + 2; R is above, so y ≥ −¼x + 2. Line 3: through (5,5) and (8,0) has gradient 0−58−5= −53, giving y = …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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