## Other Topics:

Question 1

Locate and classify all maxima and minima of the function

f(x) = 1/x 1/x2 (5 x 5)
Include a sketch of its graph with your analysis.
Question 2

Find the minimum value of C = x + 10y subject to xy = 10 (x and y both positive). To what valuies of x and y does this minimum correspond?

Question 3

Find x and y that minimize

C = 30,000x + y
subject to
40,000,000 = 4x0.1y (x > 0, y > 0).
(Round x and y to the nearest whole number.) What is the corresponding value of C?
Question 4

The demand q (in weekly sales) for Hofstra lacrosse shorts at the HU Bookstore depends on the price p according to the demand equation

q = 360 / p1.5.
If shorts cost the HU Bookstore \$8 each, how much should the bookstore charge to maximize profit?

Question 5

A quadratic regression based on old sales data reveals the following demand equation for "E = mc2" T shirts.

q = 2p2 + 33p (9 p 15)
Here, p is the price the club charges per T shirt, and q is the number the Physics Club can sell each day at the flea market.

(a) How much should the Physics Club charge for the T shirts in order to obtain the maximum revenue? What will this revenue be?

(b) Actually, the Physics club pays \$8 per T shirt (see Question 1), as well as a daily \$100 fee for using the flea market, and the would like the profit to be as large as possible. How much should they be charging to accomplish this? (Round the answer to the nearest \$1.)

(c) Predict the daily profit the club will make from the sale of T shirts at that price.

Question 6

Your Coffee House "After-Theater Chit-Chat" features two entertainers: André Rezig and fabulous Fiadora Fuffi. Costs can be broken down as follows:

 Rent: \$50 per day Salaries: \$300 per day André Rezig: \$200 per hour Fiadora Fuffi : \$250 per hour

Each artist draws varying numbers of guests, and you have calculated (using data-based regression on your graphing calculator) that, if Rezig performs for x hours and Fuffi for y hours, the number of guests they will draw is given by

g = 20x0.2y0.8.

Assuming you want to fill your establishment to its capacity of 100 customers at a minimum (daily) cost, how many hours should you have each artist perform? (Round answers to the nearest hour.)

† Actually, the function g is known as a "Cobb-Douglas Production Function," and it is indeed possible to use regression methods using your graphing calculutor -- See p. 661 in Calculus Applied to the Real World to find out how to do it.