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.
I have managed to do:
A) Find the formula for c(x), the total cost for the production of x units of the good. c(x) = 3x + 30,000.
B) Find a formula for the company's average cost per unit, a(x). a(x) = (3x+30,000)/(x).
C) Graph y=a(x) for 0 < x ≤ 50,000, 0 ≤ y ≤ 10. Label the horizontal asymptote.
I get stuck on these though:
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 the 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.
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