The solution for minimizing the function z =x+ y under an L.P.P. with constraints x+ y 2, x+2 y 8, y 3, x, y 0 is

Step-by-step solution

The objective function z = x + y is minimized subject to the constraints x + y 2 , x + 2y 8 , y 3 , x 0 , and y 0 . The feasible region is bounded and a polygon with corner points at (0,2) , (2,0) , (8,0) , (2,3) , and (0,3) . Evaluating z at these points: z(0,2) = 2 , z(2,0) = 2 , z(8,0) = 8 , z(2,3) = 5 , and z(0,3) = 3 . The minimum value is 2 , occurring at (0,2) and (2,0) . By the Fundamental Theorem of Linear Programming, every point on the line segment between (0,2) and (2,0) minimizes z . The feasible regio