Question

A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells x shirts can be found using the function f(x)=7x-40. Find and interpret the given function values and determine an appropriate domain for the function.

Answer 1

The profit function f(x)=7x-40 where x is the number of shirts sold has a domain where x is greater than or equal to zero. Selling 5 shirts results in a loss, and the company begins to make a profit at the sale of 6 shirts.

Step-by-step explanation:

The student's question involves solving and interpreting a linear function that represents the profit a company makes from selling shirts. The profit function is given as f(x)=7x-40, where x represents the number of shirts sold. To determine an appropriate domain for the function, we should consider that the company cannot sell a negative number of shirts, so x should be greater than or equal to zero. Moreover, x could be restricted further by the company's production capacity or market demand.

Let's interpret the function for specific values. If the company sells 5 shirts (x=5), we insert this value into the function to get f(5)=7(5)-40=35-40=-5. This means that if they sell 5 shirts, they would make a profit of negative $5, which is actually a loss.

Now, let's consider the domain of the function for practical purposes. Since the company makes a loss when selling less than 5.7143 shirts (since 7x=40 at the break-even point), we could say the domain of the function where the company makes a profit is x > 5.7143. However, for discrete numbers of shirts, the profitable domain would start at 6 shirts (since you can't sell a fraction of a shirt).