(9 points)
A company finds that their total production costs for a certain item are modeled by
$C(x) = 27 + 1.44 \ln(5x + 1)$
hundred dollars, where x is the number of cases of the item that are produced.
(a) The fixed cost of this production is $
When 20 cases of the item are produced, the total production cost is $
(round to the
nearest whole dollar). This means that when 20 cases are produced the average cost is $
per case (round to the nearest cent)
(b) If the total cost of a production run is about $3500 then we expect the production level will be at
cases (round to nearest whole number)
(c) Suppose that cases of the items are sold at a price of $91.79 for each case. When 70 cases are produced and sold, the revenue will be $
and the
company's profit will be $