The function C (x) = 600x - 0.3x2 represents total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold.

C (x) = 600x-0.3x²

1) we calculate the first derivative

C' (x) = 600-0.6x

2) We math the firts derivative to 0; and we find out the value of "x"

600-0.6x=0

-0.6x=-600

x=-600/-0.6

x=1000

3) we calculate the second derivative:

C'' (x) = - 0.6; because - 0.6>0; we have a maximun at x=1000.

4) We find out the maximum cost.

C (1000) = 600 (1000) - 0.3 (1000) ²

C (1000) = 600000-300000

C (1000) = 300000

Answer: the maximum cost is $300000