Mid Town Sports Apparel, Inc, has found that it needs to sell golr hats for $\$ 2.96$ each in order to be competitive. It costs $\$ 2.03$ to produce each hat, and the business has weekly overhead costs of $\$ 4000$. Complete parts (a) through (c) betow.
(a) Let $x$ be the number of hats produced each week. Express the average cost (including overhead costs) of producing one hat as a function of $x$.
\[
c(x)=\square
\]
Answer
\(\boxed{c(x) = 2.03 + \frac{4000}{x}}\)
Step 1 ：Let $x$ be the number of hats produced each week. The cost of producing one hat is $2.03. However, there are also overhead costs of $4000 per week. Therefore, the total cost of producing x hats is $2.03x + $4000.
Step 2 ：The average cost of producing one hat is then this total cost divided by the number of hats, x. This gives us the function $c(x) = (2.03x + 4000) / x$.
Step 3 ：Simplify the function to get the final answer: $c(x) = 2.03 + \frac{4000}{x}$
Step 4 ：\(\boxed{c(x) = 2.03 + \frac{4000}{x}}\)
