The maximum value of z = 6x +8y subject to x - y ≥ 0 , x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0 is…..

Step-by-step solution

We have, z = 6x +8y Subject to constraints x - y ≥ 0 , x + 3 y ≤ 12 , x ≥ 0 , y ≥ 0 . On taking given constraints as equations, we get the following graph Intersecting point of the line x - y = 0 and x + 3 y = 12 is B (3, 3). Here, OABO is the required feasible region Whose corner points are O (0, 0), A (12, 0) and B (0, 4) Now, Corner points Z = 6 x + 8 y O (0, 0) 6 × 0 + 8 × 0 = 0 A (12, 0) 6 × 12 + 8 × 0 = 72 (maximum) B (3, 3) 6 × 3 + 8 × 3 = 42 ∴ Maximum value of Z is 72.