The Physics Club sells E = mc 2 T-shirts at the local flea market. Unfortunately

Question

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  ? up down by about  % per 1% increase in the price.

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

What will the revenue be?
$

Explanation / Answer

q = 2p^2 + 33p
dq/dp = -4p + 33

E(d) = p(-4p+33)/q = (-4p^2+33p)/ q

b)
set p=10
q = -2p^2+33p = -2(10)^2 + 33(10) = -200+330 = 130
E(d) = (-400+330) / 130 = -70/130 = -0.5385

c)
Revenue = qp
R = (-2p^2+30p)p
Revenue = -2p^3 + 30p^2
dR/dp = -6p^2 + 60p = 0
6p(-p+10) = 0
p=10 ---- price to be charged for maximum revenue $10

d^2R/dp^2 = -12p < 0, so revenue has been maximized

Maximum Revenue = -2p^3 + 30p^2
= -2(10)^3 + 33(10)^2 = $1,300 answer

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