The latest demand equation for your \"Banjos Rock\" T-shirts is given by q = 60

Question

The latest demand equation for your "Banjos Rock" T-shirts is given by

q = 60x + 2400

where q is the number of shirts you can sell in one week if you charge x dollars per shirt. When you charge x dollars per shirt, your weekly cost function (in dollars) is given by

C(x) = 600x + 31500

(a) Find the weekly profit as a function of the price per shirt x.

_________

(b) Determine the unit price you should charge to break even. Enter the smaller value first.
You break even, when you charge ______ or ______ dollars per shirt.
When you set the price per shirt to one of these values, your profit is ______ dollars.

_________

Explanation / Answer

Profit, P(x)=Revenue,R(x)-C(x)

P(x)=x(-60x+2400)-(-600x+31500)= -60x2+3000x-31500

b. Break even, R(x)=C(x)

-60x2+2400x=-600x +31500

-60x2+3000x-31500=0

(x-15)(x-35)=0

x=15,35

On setting either of these values, profit =0

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