1. An efficiency study of the morning shift at a factory indicates that an average worker who starts at 08:00 A.M. will have produced $Q(t) = t^3 + 9t^2 + 12t$ units t hours later. At what time during the morning is the worker performing most efficiently?
2. MARGINAL ANALYSIS. The profit obtained from producing x thousand units of a particular commodity each year is P(X) Dollars, where $-x^{9/2} + 90x^{7/2} - 5,000$
a) Find the marginal profit $p'(x)$, and determine all values of x such that $p'(x) =0$.
b) Sketch the graph of marginal profit along with the graph $p'(x)$ on the same coordinate plane.
c) Find $p''(x)$, and determine all values of x such that $p''(x)=0$. How are these levels of production related to the graph of marginal profit?
3. ADVERTISING. The manager of the footloose sandal company determines that t months after initiating an advertising campaign, S(t) hundred pairs of sandals will be sold, where
$S(t) = \frac{3}{t+2} - \frac{12}{(t+2)^2} + 5$
a) Find $S''(T)$.
b) At what time will sales be maximized? what is the maximum level of sale?
c) The manager plans to terminate the advertising campaign when the sales rate is minimized. When does this occur? what are the sales level and sales rate at this time?
