Question

The function c(x)=400x-0.2x^2 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?

One thousand units have the minimum cost of $200000

One thousand units have the maximum cost of $200000

Two thousand units have the minimum cost of $800000

Two thousand units have the maximum cost of $800000

Answer 1

The first one is true. Plugging in 1000 units for x gives c(x) = 200000, which is the minimum the company can sell it for while still making a profit.

It can't be the maximum as the company will want to make a profit. 

The third and fourth have mathematical errors. Both will equal 0 and not 800000.

Answer 2

c(1000)=400(1000)-.2$(1000)^{2}$
c(1000)=400,000-200,000=200,000

c(2000)=400(2000)-.2$(2000)^{2}$
c(2000)=800,000-800,000=0

So, 1000 units is going to cost $200,000.  I'm not sure how that works with minimum and maximum since it is an exact answer.

Hope that helps though.