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Brilliant_brown [7]
3 years ago
7

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 sel

l 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.
Business
1 answer:
Fynjy0 [20]3 years ago
7 0

Answer:

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

P(x)=R(x)-C(x)

There are two parts

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

R(x)=Q(x)\times x

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

R(x)=(-30x+7200)\times x=7200x-30x^2

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

C(x)=567000-1800x

Putting this together we have

P(x)=R(x)-C(x)=7200x-30x^2-567000+1800x\\P(x)=-30x^2+9000x-567000

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