Answer
a. $C(x)=300000+30x$
b. $\bar C(x)= 30+\frac{300000}{x}$
c. $\bar C(1000)= 330$, $\bar C(10000) =60$, $\bar C(100000)= 33$
d. $\bar C=30$. See explanations.
Work Step by Step
a. Based on the given conditions, we have
$C(x)=300000+30x$
b. The average cost is given by
$\bar C(x)=\frac{300000+30x}{x}=30+\frac{300000}{x}$
c. (i) Using the given values, we have
$\bar C(1000)=30+\frac{300000}{1000}=30+300=330$ dollars
(the average cost to produce 1000 shoes is 330 dollars).
(ii) Similarly, we have
$\bar C(10000)=30+\frac{300000}{10000}=30+30=60$ dollars
(the average cost to produce 10000 shoes is 60 dollars).
(iii) $\bar C(100000)=30+\frac{300000}{100000}=30+3=33$ dollars
(the average cost to produce 100000 bikes is 33 dollars).
d. The horizontal asymptote can be found by letting $x\to\infty$ which gives $\bar C=30$. This means that when the number of shoes produced is extremely large, the average cost will be close to 30 dollars.
