Answer:
The vertex that maximize the problem is (2,000,4,000)
Explanation:
we have

The vertex of the shaded region are
A(0,0), B(4,000,0),C(2,000,4,000), D(0,6,000)
Substitute the value of x and the value of y of each vertex in the z equation to find the solution
case A) A(0,0)

case B) B(4,000,0)

case C) C(2,000,4,000)

case D) D(0,6,000)

therefore
The vertex that maximize the problem is (2,000,4,000)