Answer
(a.) $C(x)=300,000+10x$
(b.) $\bar{C}(x)=\frac{300,000+10x}{x}$.
(c.) $20,000$ players.
Work Step by Step
Fixed monthly cost $=\$300,000$.
Cost of each player $=\$10$.
Number of players $=x$.
(a.)
Cost function is equal to fixed monthly cost plus total cost of $x$ players.
$\Rightarrow C(x)=300,000+10x$
(b.) Average $=\frac{Total \;cost}{Number \;of \; players}$
$\Rightarrow \bar{C}(x)=\frac{C(x)}{x}$
$\Rightarrow \bar{C}(x)=\frac{300,000+10x}{x}$
Hence, the average cost function is
$\bar{C}(x)=\frac{300,000+10x}{x}$.
(c.) Replace $\bar{C}(x)$ by $25$. into the average cost function.
$\Rightarrow 25=\frac{300,000+10x}{x}$
Multiply both sides by $x$ to clear fractions.
$\Rightarrow 25x=x\cdot \left (\frac{300,000+10x}{x}\right )$
Simplify.
$\Rightarrow 25x=300,000+10x$
Subtract $10x$ from both sides.
$\Rightarrow 25x-10x=300,000+10x-10x$
Simplify.
$\Rightarrow 15x=300,000$
Divide both sides by $15$.
$\Rightarrow \frac{15x}{15}=\frac{300,000}{15}$
Simplify.
$\Rightarrow x=20,000$.
