HW 18 Intro to Exponential Functions and Logarithms: Problem 13
(9 points)
A company finds that their total production costs for a certain item are modeled by
C(z) = 35 + 1.48 ln(3z + 1)
hundred dollars, where \(z\) is the number of cases of the item that are produced.
(a) The fixed cost of this production is $ \boxed{} When 20 cases of the item are produced, the total production cost is $ \boxed{} (round to the nearest whole dollar). This means
that when 20 cases are produced the average cost is $ \boxed{} per case (round to the nearest cent).
(b) If the total cost of a production run is about $4300 then we expect the production level will be at \boxed{} cases (round to nearest whole number).
(c) Suppose that \boxed{} cases of the items are sold at a price of $134.29 for each case. When 59 cases are produced and sold, the revenue will be $ \boxed{} and the company's
profit will be $ \boxed{}
Note: You can earn partial credit on this problem.
