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).
To find the polynomial R(p) that represents the total revenue when the shirts are p dollars each, we need to multiply the price per shirt by the quantity of shirts sold.
Given that the vendor expects to sell 2000 - 100p shirts at a tournament, the formula for the total revenue R(p) can be calculated as:
R(p) = (2000 - 100p) * p
Simplifying the expression:
R(p) = 2000p - 100p^2
Now, let's find R(5), R(10), and R(20).
To find R(5), substitute p = 5 into the equation:
R(5) = 2000 * 5 - 100 * 5^2
R(5) = 10000 - 100 * 25
R(5) = 10000 - 2500
R(5) = 7500
So, R(5) is equal to 7500.
To find R(10), substitute p = 10 into the equation:
R(10) = 2000 * 10 - 100 * 10^2
R(10) = 20000 - 100 * 100
R(10) = 20000 - 10000
R(10) = 10000
So, R(10) is equal to 10000.
To find R(20), substitute p = 20 into the equation:
R(20) = 2000 * 20 - 100 * 20^2
R(20) = 40000 - 100 * 400
R(20) = 40000 - 40000
R(20) = 0
So, R(20) is equal to 0.
Therefore, the polynomial R(p) representing the total revenue when the shirts are p dollars each is R(p) = 2000p - 100p^2, and when p = 5, R(5) = 7500, when p = 10, R(10) = 10000, and when p = 20, R(20) = 0.