The maximum value of 2 x + y subject to 3 x + 5 y ≤ 26 and 5 x + 3 y ≤ 30 , x ≥ 0 , y ≥ 0 is

Question

The maximum value of 2 x + y subject to 3 x + 5 y ≤ 26 and 5 x + 3 y ≤ 30 , x ≥ 0 , y ≥ 0 is, 12, 11.5, 10, 17.33

MARKS App · Accepted Answer

3 x + 5 y = 26.... ( i ) × 5 5 x + 3 y = 30.... ( i i ) × 3 15 x + 25 y = 130 15 x + 9 y = 90 16 y = 40 y = 40 16 = 5 2 ∴ 3 x + 5 × 5 2 = 26 3 x = 26 − 25 2 x = 9 2 z = 2 x + y Now check values of objective function at corner points of the shaded region Z A = 2 × 6 + 0 = 12 Z B = 2 × 9 2 + 5 2 = 9 + 2.5 = 11.5 Z C = 2 × 0 + 26 5 = 26 5 = 5.2 Hence Z max = 12 at x = 6 and y = 0

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