Calc questions

1.

The weekly sales of Honolulu Red Oranges is given by

q = 1116 − 18p.

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 

q = (96 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E when the price is set at $31. (Round your answer to three decimal places.)

E = ___________

 (b) At what price should tissues be sold in order to maximize the revenue? (Round your answer to the nearest cent.)$____________ (c) Approximately how many cases of tissues would be demanded at that price? (Round your answer to the nearest whole number.)_________ cases per week  3. 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 + 30p      (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 $9 per shirt. (Round your answer to two decimal places.) Interpret the result. The demand for E = mc2 T-shirts is going down by about _______% per 1% increase in the price. 4. 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 formq = 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 $51.00 per book, the sales amount to 10,000 per year; when the price is set at $75.00 per book, the sales drop to 1000 per year. Use these data to calculate the demand equation. q = ________ (b) Now estimate the unit price that maximizes annual revenue.$_________ Predict what Big Book Publishing, Inc.'s annual revenue will be at that price.$________