Ye National Cheese Emporium's annual profit is given by the model P(m) in tens of thousands of dollars, where m represents the number of varieties of cheese in tens that they stock in a given year. For example, the value m=1 indicates that the Emporium stocked 10 varieties of cheese.

The applet above shows the graph of P''(m). Observe that there is an input box for m that will give you the coordinates of point E on P''(m) as well as the corresponding points on P(m) and P'(m). The points B and D are the intercepts for P'(m) (showing the m values where the derivative is 0). Use the applet to answer the questions below.

Note: If you are asked about an extrema value that you determine does not exist, type NONE in all fhe associated relevant boxes.

Ye National Cheese Emporium's annual profit is gven by the model P(m) in tens of thousands of dolars, where m represents the number of varieties of cheese in tens that they stock in a given year. For example, the value m=1 indicates that the Emporium stocked 10 varieties of cheese: The applet above shows the graph of P(m) Observe that there is an input box for m that witi give you the coordinates of point E on P(m) as well as the corresponding points on P(m) and P(m). The points B and D are the intercepts for P(m) (showing the m values where the derivative is 0 ) Use the applet to answer the questions below. Note ll you are osted obout an extreme volue that you determine does not exst, fype NONE in ail the associated ond relivant baxes (a) According to the graph the function P(m) has a domain of (use intervol notation) Thus the Emporium's profit model is valid when they stock between varieties and varietes of cheese. (b) Suppose that when the Emporium stocks 130 varieties of cheese, their anmal revenue is 182.23 ten thousand dollars. The profit model implies that the annual profit when the Emporium stocks 130 varieties of cheese is ten thousand dotlars. Thus, their annual cost to stock 130 varieties of cheese must be ten thousand dollars. (c) The critical numbers of P(m) are (list critical values; separated by commas). For each of these critical numbers; the Emporium's annual profit was changing at a rate of dollars per each 10 additionat cheese varieties stocked. (d) The Emporium's profit increasts from m i to m and then increases again fiom m = Emporium's profit is decreasing from m= to m= to The (e) Using the second derivative test, the Emporium had a relative minimum profit of ten thousand dollars when varieties of cheese were stocked, since P is Again, using the second derivative test, the Emponium had a relative maximum profit of ten thousand dollars when varieties of cheese were stocked, since P(10) is (f) When varieties of cheese are stocked in a year, the Emporium has an absolute maximum profit of ten thousand dollars By way of compatison, the Emporium's absolute minimum profit is ten thousand dollars when m=