The difference between the maximum value and minimum value of the objective function z = 3x + 5y of a linear programming problem subject to constraints 5x + 10y 50 , x + y 1 , y 4 and x 0, y 0 is 3 . Then the value of is

Step-by-step solution

The given constraints are: 5x + 10y 50 x + 2y 10 x + y 1 y 4 x 0, y 0 The feasible region is bounded by the lines x + 2y = 10 , x + y = 1 , y = 4 , x = 0 , and y = 0 . Let us find the corner points of this feasible region: Intersection of x = 0 and x + y = 1 (0, 1) Intersection of x = 0 and y = 4 (0, 4) Intersection of y = 4 and x + 2y = 10 x + 8 = 10 x = 2 (2, 4) Intersection of y = 0 and x + 2y = 10 x = 10 (10, 0) Intersection of y = 0 and x + y = 1 x = 1 (1, 0) Now, we evaluate the objective function z = 3x + 5y