The maximum value of z = 4x + y subject to the constraints x + y 5, 2x + y 7, 3x + 2y 11, x 0, y 0 is

Step-by-step solution

The given constraints are: x + y 5 2x + y 7 3x + 2y 11 x 0, y 0 To find the corner points of the feasible region, we determine the intersection points of the boundary lines with each other and with the coordinate axes, and check if they satisfy all constraints. 1) Intersection of 2x + y = 7 with the x-axis ( y = 0 ) gives x = 3.5 . The point is (3.5, 0) . Checking in other constraints: 3.5 + 0 = 3.5 5 (True), 3(3.5) + 0 = 10.5 11 (True). 2) Intersection of x + y = 5 with the y-axis ( x = 0 ) gives y = 5 . The point