Chapter 5.5, Problem 91PE

The monthly sales of winter coats follow a periodic cycle with sales peaking late in the year and before the winter holidays. The monthly sales total $S\left(\text{in \$1000}\right)$ is given by

$s\left(t\right)=350\cos \left(\frac{\pi }{6}t+\frac{\pi }{6}\right)+500$

where $t$ is the month number $\left(t=1\text{ corresponds to January}\right).$

a. Write the range of this function in interval notation.

b. During which months $\left(0\le t\le 12\right)$ are sales at their maximum?

c. During which months $\left(0\le t\le 12\right)$ are sales at their minimum?

d. In which months, between $1$ and $12$ inclusive, are the sales $\text{\$}675,000$ ?