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.

Question

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?
Responses

A all real numbersall real numbers

B {0 ≤ x ≤ 600}{0 ≤ x ≤ 600}

C {0 ≥ x ≥ 600}{0 ≥ x ≥ 600}

D {-1,200 ≤ x ≤ 2,000}{-1,200 ≤ x ≤ 2,000}

E {-1,200 ≤ x ≤ 12,000}

Answer 1

In the context of Henry's t-shirt printing business, the variable \( x \) represents the number of shirts sold. Since Henry ordered 600 shirts, the maximum number of shirts he can sell is 600. He cannot sell a negative number of shirts, and therefore the minimum number of shirts he can sell is 0.

Thus, the domain for this profit function is defined by the condition that \( x \) must be between 0 and 600, inclusive.

Therefore, the correct answer is:

B {0 ≤ x ≤ 600}