(Solved): ( 9 points) A company finds that their total production costs for a certain item are modeled by \[ ...

( 9 points) A company finds that their total production costs for a certain item are modeled by \[ C(x)=24+1.49 \ln (3 x+1) \] hundred dollars, where \( x \) is the number of cases of the item that are produced. (a) The fixed cost of this production is \( \$ \) When 25 cases of the item are produced, the total production cost is \( \$ \) (round to the nearest whole dollar). This means that when 25 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 \( \$ 3200 \) 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 \( \$ 69.29 \) for each case. When 72 cases are produced and sold, the revenue will be \( \$ \) and the company's profit will be \( \$ \)