Question 1

Locate and classify all maxima and minima of the function

f(x) = 1/x 1/x² (5 x 5)

Answer

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?

Answer

Find x and y that minimize

C = 30,000x + y

40,000,000 = 4x^0.1y (x > 0, y > 0).

Answer

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 / p^1.5.

Answer

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)

(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.

Answer

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 = 20x^0.2y^0.8.

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.

Answer

Stefan Waner (matszw@hofstra.edu)

Steven R. Costenoble (matsrc@hofstra.edu)

Last Updated:May, 1997 Copyright © 1996 StefanWaner and Steven R. Costenoble