A firm manufactures a commodity at two different factories, Factory X and Factory Y. The total cost in dollars of manufacturing depends on the quantities, x and y, produced at each factory, respectively, and is expressed by the joint cost function: C(x, y) = 2x^2 + xy + 4y^2 + 1600.
If the company's objective is to produce 500 units per month while minimizing the total monthly cost of production, how many units should be produced at each factory? (Round your answer to the nearest whole number.)
Units to be produced to minimize costs:
x = units at Factory X.
Enter a whole number.
y = units at Factory Y.
Enter a whole number.
Now determine the minimum cost. Minimal cost.