The minimum value of z = 5x - 7y , subject to the constraints x + y ≤ 7 , 2x - 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0 , is: - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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The minimum value of z = 5 x - 7 y, subject to the constraints x + y \leq 7, 2 x - 3 y + 6 \geq 0, x \geq 0, y \geq 0, is:

Solution & Step-by-step Explanation

Corner points of feasible region:Intercepts of x + y = 7 : (7, 0), (0, 7) .Intercepts of 2 x - 3 y = - 6 : (- 3, 0) [Not in region], (0, 2) .Intersection of x + y = 7 and 2 x - 3 y = - 6 : 2 (7 - y) - 3 y = - 6 ⟹ 14 - 5 y = - 6 ⟹ 5 y = 20 ⟹ y = 4, x = 3 . Point (3, 4) .Vertices: (0, 0), (7, 0), (3, 4), (0, 2) . Z (0, 0) = 0 Z (7, 0) = 35 Z (3, 4) = 5 (3) - 7 (4) = 15 - 28 = - 13 Z (0, 2) = 0 - 7 (2) = - 14 .Minimum value is - 14 .

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The minimum value of z = 5 x - 7 y, subject to the constraints x + y \leq 7, 2 x - 3 y + 6 \geq 0, x \geq 0, y \geq 0, is:

2

- 10

- 13

- 14

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