Preview Activity 5.4.1.
A drug company estimates that to produce a new drug, it will cost $5 million in startup resources, and that once they reach production, each gram of the drug will cost $2500 to make.
(a)
Determine a formula for a function \(C(q)\) that models the cost of producing \(q\) grams of the drug. What familiar kind of function is \(C\text{?}\)
(b)
The drug company needs to sell the drug at a price of more than $2500 per gram in order to at least break even. To investigate how they might set prices, they first consider what their average cost per gram is. What is the total cost of producing \(1000\) grams? What is the average cost per gram to produce \(1000\) grams?
(c)
What is the total cost of producing \(10000\) grams? What is the average cost per gram to produce \(10000\) grams?
(d)
Our computations in (b) and (c) naturally lead us to define the “average cost per gram” function, \(A(q)\text{,}\) whose output is the average cost of producing \(q\) grams of the drug. What is a formula for \(A(q)\text{?}\)
(e)
(f)
What can you say about the long-range behavior of \(A\text{?}\) What does this behavior mean in the context of the problem?
This activity is based on p. 457ff in Functions Modeling Change, by Connally et al.
