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 ? up down 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?

$ ________