Question

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..

Answer 1

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. 

Answer 2

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