The difference between the maximum value and minimum value of objective function z =3 x+5 y subject to constraints x+3 y 60 , x+ y 10, x- y =0, x, y 0 is

Step-by-step solution

Feasible region determination The objective function z = 3x + 5y is subject to constraints: x + 3y 60 , x + y 10 , x = y , and x 0 , y 0 . Substituting x = y into the inequality constraints yields 4y 60 and 2y 10 , simplifying to 5 y 15 . With x = y , the non-negativity conditions are satisfied. The feasible region is the line segment from (5,5) to (15,15) . Evaluation of objective function The function values at the endpoints are: z(5,5) = 3(5) + 5(5) = 40 z(15,15) = 3(15) + 5(15) = 120 The minimum value is 40 and