Question

Max ($15x + $20 y) s.t. 8x + 5y ≤ 40 4x + y ≥ 8 You solve the problem graphically and the optimum solution is at the corner point where the above 2 constraints intersect. What is the maximum revenue at the optimal solution?

Answer 1

The maximum revenue at the optimal solution is obtained by graphically solving the constraints 8x + 5y ≤ 40 and 4x + y ≥ 8, finding the intersecting corner point, and substituting these x and y values into the revenue equation $15x + $20y.

Step-by-step explanation:

To find the maximum revenue at the optimal solution using graphical methods, we need to identify the corner point where the two constraints intersect. The constraints given are 8x + 5y ≤ 40 and 4x + y ≥ 8.

1. Graph the constraints on a coordinate plane, marking the feasible region defined by the inequalities.
2. Identify the corner points of the feasible region.
3. Calculate the objective function, which is the revenue $15x + $20y, at each corner point.

The optimal solution occurs at the intersection of the two constraints. To find the intersection, we can solve the system of equations:

8x + 5y = 40

4x + y = 8

By solving these equations simultaneously, we would find the values of x and y that give us the intersecting point. Once we have x and y, we substitute these into the objective function $15x + $20y to find the maximum revenue.

Assuming we have solved the equations and found the intersection point to be, for example, (x,y), the maximum revenue is calculated as $15x + $20y.