The maximum value of Z = 4x + 5y , subject to the constraints 3x + y 15, 3x + 4y 24, x 0, y 0 is

Step-by-step solution

The given constraints are 3x + y 15 , 3x + 4y 24 , x 0 , y 0 . To find the corner points of the feasible region, we solve the equations of the boundary lines: 3x + y = 15 3x + 4y = 24 Subtracting the first equation from the second gives: 3y = 9 y = 3 Substituting y = 3 in the first equation: 3x + 3 = 15 3x = 12 x = 4 The intersection point is (4, 3) . The corner points of the feasible region are the origin (0, 0) , the valid x-intercept (5, 0) , the intersection point (4, 3) , and the valid y-intercept (0, 6) . Eva