# Calculus exam help

1.

The weekly sales of Honolulu Red Oranges is given by

Calculate the price elasticity of demand when the price is $31 per orange (yes, $31 per orange). Elasticity = ______

Interpret your answer.

The demand is going down by ______% per 1% increase in price at that price level.

Also, calculate the price that gives a maximum weekly revenue.

$_________

Find this maximum revenue.

$_______

2.

The consumer demand equation for tissues is given by

^{2}, where

*p*is the price per case of tissues and

*q*is the demand in weekly sales.

*E*when the price is set at $31. (Round your answer to three decimal places.)

*E*= ___________

*E*=

*mc*

^{2}T-shirts at the local flea market. Unfortunately, the club’s previous administration has been losing money for years, so you decide to do an analysis of the sales. A quadratic regression based on old sales data reveals the following demand equation for the T-shirts: q = −2p

^{2}+ 30p (9 ≤ p ≤ 15).

*p*is the price the club charges per T-shirt, and

*q*is the number it can sell each day at the flea market.

*E*=

*mc*

^{2}T-shirts.

*E*=

*mc*

^{2}T-shirts is going down by about _______% per 1% increase in the price.

*Big Book Publishing, Inc.*, and you have been approached to determine the best selling price for the hit calculus text by Whiner and Istanbul entitled

*Fun with Derivatives*. You decide to make life easy and assume that the demand equation for

*Fun with Derivatives*has the linear form

*q*=

*mp*+

*b*, where

*p*is the price per book,

*q*is the demand in annual sales, and

*m*and

*b*are certain constants you must determine.

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