Chapter 4.6, Problem 42E

Revenue from Seasonal Merchandise The revenue received from the sale of electric fans is seasonal, with maximum revenue in the summer. Let the revenue (in dollars) received from the sale of fans be approximated by

$R\left(t\right)=120\cos 2\pi t+150$,

where $t$ is time in years, measured from July 1.

a. Find $R^{\text{'}}\left(t\right)$.

b. Find $R^{\text{'}}\left(t\right)$ for August 1. (Hint: August 1 is $1/12$ of a year from July 1.)

c. Find $R^{\text{'}}\left(t\right)$ for January 1.

d. Find $R^{\text{'}}\left(t\right)$. For June 1.

e. Discuss whether the answers in part b-d are reasonable for this model.