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 range of this function in this context?
Responses
A {0 ≤ p ≤ 500}{0 ≤ p ≤ 500}
B {0 ≥ p ≥ 500}{0 ≥ p ≥ 500}
C {-1,200 ≤ p ≤ 2,000}{-1,200 ≤ p ≤ 2,000}
D {-1,200 ≤ p ≤ 12,000}{-1,200 ≤ p ≤ 12,000}
E {-1,200 ≥ p ≥ 12,000}
To find the range of the profit function, we need to determine the minimum and maximum values that p can take on.
The given profit function is p = 22x - 1200, where x represents the number of shirts sold.
We know that x represents the number of shirts sold and cannot be negative, so the minimum value for x is 0.
To find the maximum value for x, we need to determine how many shirts Henry orders. He orders 600 shirts, so the maximum value for x is 600.
Substituting these values into the profit function, we have:
p = 22(0) - 1200 = -1200
p = 22(600) - 1200 = 12000
Therefore, the range of the function is {-1,200 ≤ p ≤ 12,000}.
The answer is D.