The maximum value of Z=10 x+16 y , subject to constraints x 0, y 0, x+y 12,2 x+y 20 is

Step-by-step solution

The feasible region is defined by the constraints x 0 , y 0 , x + y 12 , and 2x + y 20 . The corner points of the feasible region are found by solving the intersection of the boundary lines: 1. Intersection of x=0 and y=0 gives (0, 0) . 2. Intersection of x=0 and x+y=12 gives (0, 12) . 3. Intersection of y=0 and 2x+y=20 gives (10, 0) . 4. Intersection of x+y=12 and 2x+y=20 : Subtracting the first from the second gives x = 8 . Substituting x=8 into x+y=12 gives y = 4 . So, the point is (8, 4) . Evaluate Z = 10x + 16