The function C (x) = 400x - 0.2x2 represents the 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. Which statement is true?. A. One thousand units have the minimum cost of $200,000 ... B. One thousand units have the maximum cost of $200,000 ... C. Two thousand units have the minimum cost of $800,000 ... D. Two thousand units have the maximum cost of $800,000 ...

The correct answer to this question is letter " B. One thousand units have the maximum cost of $200,000."

C (x) = 400 - 0.2x^2

0 = 400 - 0.2^2

0.2x^2 = 400

x^2 = 2000

dC (x) / dt = 400 - 0.4 x = 0

C (x) = (400) (1000) - 0.2 (1000²) = $ 200,000

To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0.

C (x) = 400x - 0.2x²

dC (x) / dt = 400 - 0.4 x = 0

The value of x is 1000. This is the value of the maxima. As the value of C (x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation,

C (x) = (400) (1000) - 0.2 (1000²) = $ 200,000

Thus, the answer is letter B.