The solution set for minimizing the function z =x+ y with constraints x+ y 2, x+2 y 8, y 3, x, y 0 contains

Step-by-step solution

Linear programming is used to minimize the function z = x + y subject to the constraints: x + y 2 , x + 2y 8 , y 3 , x 0 , and y 0 . The feasible region is a convex polygon whose corner points are (2,0) , (8,0) , (2,3) , (0,3) , and (0,2) . Evaluating the objective at each corner gives z(2,0)=2 , z(8,0)=8 , z(2,3)=5 , z(0,3)=3 , and z(0,2)=2 . The minimum value is 2 , achieved at both (2,0) and (0,2) . Since these are adjacent vertices, all points on the line segment connecting them—where x + y = 2 with 0 x 2 and 0