Chapter 11, Problem 18RQ

We have decided to become entrepreneurs by raising turkeys for the Thanksgiving holiday. We already have purchased some land in the country with buildings on it, so that expense need not be a part of our analysis. A study of the way turkeys grow indicates that the mass of a turkey (m) from the time it hatches (at time zero) until it reaches maturity is:

$m=K\left(1-e^{-bt}\right)$

Here, we select values of K and b depending on the breed of turkey we decide to raise. The value (V) of our turkey is simply the mass of the turkey times the value per pound-mass (S) when we sell it, or:

$V=Sm$

Here, S is the value per pound-mass (in dollars). Finally, since we feed the turkey the same amount of food each day, the cumulative cost (C) to feed the bird is:

$C-Nt$

Here, A is the cost of one day’s supply of food [$/day].

Create a graph of this situation, showing three lines: cumulative food cost, bird value, and profit on a particular day. For the graph, show the point after which you begin to lose money, and show the time when it is most profitable to sell the bird, indicating the day on which that occurs. Use values of K = 21 pound-mass, b = 0.03 per day S = $1 per pound-mass, and N = $0.12 per day.