Question

Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200.

Henry orders 600 shirts and determines that the profit for his new business is modeled by the function P = 22x - 1200. What is the domain of this function in this context?
A) all real numbers
B) {0 ≤ x ≤ 600}
C) {0 ≥ x ≥ 600}
D) {-1,200 ≤ P ≤ 2,000}

Answer 1

Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200

Answer 2

Option: B is the correct answer.

B) {0 ≤ x ≤ 600}

Explanation:

We are given a profit function in terms of x where x is the number of shirts ordered as follows:

`P=22x-1200`

Now, we know that the domain of a function are the possible values of the independent variable for which a function is defined i.e. the possible values of x for which P is defined.

x has to be greater than equal to 0.

i.e. either none of the t-shirts are ordered or some.

and x has to be less than or equal to 600.

Hence, the domain is:

0 ≤ x ≤ 600