Answer
a. $C(x)=50000+25x$
b. $\bar C(x)= 25+\frac{50000}{x}$
c. $\bar C(50)= 1025$, $\bar C(100) =525$, $\bar C(1000)=75$, $\bar C(100,000)=25.5$ dollars; see explanations.
d. $\bar C=25$ dollars
Work Step by Step
a. Based on the given conditions, the cost function can be written as $C(x)=50000+25x$
b. The average cost function can be written as
$\bar C(x)=\frac{C}{x}=\frac{50000+25x}{x}=25+\frac{50000}{x}$
c. For $x=50$, we have
$\bar C(50)=25+\frac{50000}{50}=25+1000=1025$ dollars
which represents the average cost when producing 50 graphing calculators.
For $x=100$, we have
$\bar C(100)=25+\frac{50000}{100}=25+500=525$ dollars
which represents the average cost when producing 100 graphing calculators.
For $x=1000$, we have
$\bar C(1000)=25+\frac{50000}{1000}=25+50=75$ dollars
which represents the average cost when producing 1000 graphing calculators.
For $x=100,000$, we have
$\bar C(100,000)=25+\frac{50000}{100000}=25+0.5=25.5$ dollars
which represents the average cost when producing 100,000 graphing calculators.
d. The horizontal asymptote can be found by letting $x\to\infty$, which gives $\bar C=25$ dollars, which represents the average cost when producing an unlimited number of graphing calculators.
