## Related questions with answers

It costs a company $30,000 to begin production of a good, plus$3 for every unit of the good produced. Let x be the number of units produced by the company.

(a) Find a formula for $C(x)$, the total cost for the production of $x$ units of the good.

(b) Find a formula for the company's average cost per unit, $a(x)$.

(c) Graph $y=a(x)$ for $0<x \leq 50,000,0 \leq y \leq 10$. Label the horizontal asymptote.

(d) Explain in economic terms why the graph of $a$ has the long-run behavior that it does.

(e) Explain in economic terms why the graph of $a$ has the vertical asymptote that it does.

(f) Find a formula for $a^{-1}(y)$. Give an economic interpretation of $a^{-1}(y)$.

(g) The company makes a profit if the average cost of its good is less than $\$ 5$ per unit. Find the minimum number of units the company can produce and make a profit.

Solution

Verified## (a)

The total cost ) = (variable cost) + (fixed cost). The variable cost varies with $x$, the number of units produced.

$C(x)=3x+30,000$

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