The members of the Young Entrepreneurs Club decide to sell T-shirts in their school colors for Spirit Week. In a marketing survey, the members ask students whether or not they would buy a T-shirt for a specific price. In analyzing the data, club members find that at a price of $20 they would sell 60 T-shirts. For each $5 increase in price, they would sell 10 fewer T-shirts.
a. Find a linear function that relates the price in dollars, p, and the number of T-shirts sold, n.
b. Write a function that gives revenue as a function of price. (Use your function in 11a as a substitute for the number of T-shirts sold.)
c. Convert the revenue function to vertex form. What is the real-world meaning of the vertex?
d. If the club members want to receive at least $1050 in revenue, what price should they charge for the T-shirts?