Question

Maximize the function f(x,y)=500x+350y in the region determined by the following constraints: 3x+2y<=24, x+2y<=16, x+y<=9, x>=0, y>=0. What are the coordinates of the optimal solution?

Answer 1

To maximize the function f(x,y) = 500x + 350y within the given constraints, find the coordinates of the optimal solution.

Step-by-step explanation:

To maximize the function f(x,y) = 500x + 350y within the given constraints, we need to find the coordinates of the optimal solution.

First, we graph the region determined by the constraints. Next, we identify the feasible region where all the constraints are satisfied. Finally, we evaluate the function f(x,y) at the vertices of the feasible region and choose the coordinates that yield the maximum value.

The optimal solution occurs at the point (8, 8) and the maximum value of the function is f(8, 8) = 500(8) + 350(8) = 8400.