The difference between the maximum value and the minimum value of the objective function z = 3x + y subject to the constraints 2x + 3y 6 , x + y 1 , x 0 , y 0 is....

Step-by-step solution

The given objective function is z = 3x + y . The constraints are 2x + 3y 6 , x + y 1 , x 0 , and y 0 . The feasible region is bounded by the lines 2x + 3y = 6 , x + y = 1 , x = 0 , and y = 0 . The corner points of this feasible region can be found by finding the intersections of these lines with the coordinate axes. For 2x + 3y = 6 , the intercepts are (3, 0) and (0, 2) . For x + y = 1 , the intercepts are (1, 0) and (0, 1) . The corner points of the bounded feasible region are (1, 0) , (3, 0) , (0, 2) , and (0, 1)