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1.The weekly sales of Honolulu Red Oranges is given by

q = 1200 20p.

Calculate the price elasticity of demand when the price is $30 per orange (yes, $30 per orange). HINT [See Example 1.] Interpret your answer.

The demand is going ?updown 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 Physics Club sells E = mc² 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 = 2p² + 33p (9 p 15).

Here, p is the price the club charges per T-shirt, and q is the number it can sell each day at the flea market.

(a) Obtain a formula for the price elasticity of demand for E = mc² T-shirts. E = (b) Compute the elasticity of demand if the price is set at $10 per shirt. (Round your answer to two decimal places.) Interpret the result.

The demand for E = mc² T-shirts is going ?updown by about % per 1% increase in the price.

(c) How much should the Physics Club charge for the T-shirts to obtain the maximum daily revenue? $ What will the revenue be? $

3.The demand curve for original Iguanawoman comics is given by

q =

(441 p)2

50

(0 p 441)

where q is the number of copies the publisher can sell per week if it sets the price at $p.

(a) Find the price elasticity of demand when the price is set at $39 per copy. (Round your answer to two decimal places.) (b) Find the price at which the publisher should sell the books to maximize weekly revenue. (Round your answer to the nearest cent.) $ (c) What, to the nearest $1, is the maximum weekly revenue the publisher can realize from sales of Iguanawoman comics? $

4.You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers has the linear form q = mp + b, where p is the price per hamburger, q is the demand in weekly sales, and m and b are certain constants you must determine.

(a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 4000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to calculate the demand equation.

q =

(b) Now estimate the unit price that maximizes weekly revenue. $ Predict what the weekly revenue will be at that price. $

5.You have been hired as a marketing consultant to 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.

(a) Your market studies reveal the following sales figures: when the price is set at $50.00 per book, the sales amount to 10,000 per year; when the price is set at $80.00 per book, the sales drop to 1000 per year. Use these data to calculate the demand equation.

q =

(b) Now estimate the unit price that maximizes annual revenue. $ Predict what Big Book Publishing, Inc.'s annual revenue will be at that price. $

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