Answer
(a.) $C(x)=50,000+25x$.
(b.) $\bar{C}(x)=\frac{50,000+25x}{x}$.
(c.) $5,000$ graphing calculators.
Work Step by Step
Let the number of calculator manufactured be $x$.
Fixed monthly cost $=\$50,000$.
Cost of each calculator $=\$25$.
Total cost of calculators $=25x$.
(a.):- The cost function is equal to fixed monthly cost plus total cost of each calculator.
$\Rightarrow C(x)=50,000+25x$
(b):- Average cost function $=\frac{Total \;cost}{Number\;of \;calculators}$
$\Rightarrow \bar{C}(x)=\frac{50,000+25x}{x}$
(c):- Replace $\bar{C}(x)$ by $35$ into average cost function.
$\Rightarrow 35=\frac{50,000+25x}{x}$
Multiply both sides by $x$.
$\Rightarrow 35x=\frac{50,000+25x}{x}\cdot x$
Simplify.
$\Rightarrow 35x=50,000+25x$
Subtract $25x$ from both sides.
$\Rightarrow 35x-25x=50,000+25x-25x$
Simplify.
$\Rightarrow 10x=50,000$
Divide both sides by $10$.
$\Rightarrow \frac{10x}{10}=\frac{50,000}{10}$
Simplify.
$\Rightarrow x=5000$.
