The latest demand equation for your banjos rock t-shirts is given by q = −30x + 7200 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) = −1800x + 567000 (a) find the weekly profit as a function of the price per shirt x.

P(x)=-30x^2+9000x-567000

Explanation:

First, we need to remember the parts of a Profit function. A profit a business makes  equals revenue (R(x)) minus its costs (C(x)). So

There are two parts

1. Revenue: which is equal to the number of units sold times the price:

where x is the price you charge and Q(x) is the number of shirts that can be sold. Then

2. Cost. The cost function is directly given by the question

Putting this together we have

urban company reports the following information regarding its production cost: units produced 37,000 units direct labor $ 30 per unit direct materials $ 35 per unit variable overhead $ 237,000 in total fixed overhead $ 127,000 in total