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.
(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.
(c) how much should the physics club charge for the t-shirts to obtain the maximum daily revenue? what will the revenue be?

a)

b) -0.50

c) $7.50

Step-by-step explanation:

a)

The price elasticity of demand E at a given point is defined as

and it is supposed to measure the possible response of tissues demand due to small changes in its price when the price is at

(a) Obtain a formula for the price elasticity of demand for E = mc2 T-shirts.

Since

where

(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.

When the price is set at $9 the demand is

t-shirts

Also, we have

hence

That would mean the demand would go down about 0.5% per 1% increase in price at that price level.

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

Let T be the price at which the T-shirts are sold.

The daily revenue is Tq so Tq is maximum when q is maximum.

since  

there is a critical point when -4p + 30 = 0

and p should be (30/4) = $7.5

given that the second derivative of q with respect to p equals -4 < 0, that point is a maximum.

At that price, the demand would be

T-shirts.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

1350 hats

step-by-step explanation:

divide 900 by 2 to find 50% or half of 900

900/2=450

add 450 to 900

1350