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

Step-by-step solution

The feasible region is bounded by the lines x + 3y = 60 , x + y = 10 , x = y , and the y-axis ( x = 0 ). The corner points of the feasible region are obtained by solving the equations of the lines pairwise: 1. Intersection of x = y and x + y = 10 gives (5, 5) . 2. Intersection of x = y and x + 3y = 60 gives (15, 15) . 3. Intersection of x = 0 and x + y = 10 gives (0, 10) . 4. Intersection of x = 0 and x + 3y = 60 gives (0, 20) . Evaluating the objective function Z = 3x + 5y at these corner points: At (5, 5) , Z = 3