Selling shirts. If a vendor charges p dollars each for
rugby shirts, then he expects to sell 2000 � 100p shirts at
a tournament.
a) Find a polynomial R(p) that represents the total revenue
when the shirts are p dollars each.
b) Find R(5), R(10), and R(20).
c) Use the bar graph to determine the price that will give
the maximum total revenue.
To find the polynomial R(p) that represents the total revenue, we need to multiply the price per shirt (p) by the number of shirts sold (2000 - 100p).
a) So, R(p) = p * (2000 - 100p)
b) To find R(5), R(10), and R(20), we can substitute these values into the R(p) equation:
R(5) = 5 * (2000 - 100 * 5)
R(10) = 10 * (2000 - 100 * 10)
R(20) = 20 * (2000 - 100 * 20)
c) To determine the price that will give the maximum total revenue, we can plot the revenue values R(p) for different prices on a bar graph. The price that corresponds to the highest bar represents the price that will give the maximum total revenue.