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 can use the formula:
R(p) = p * quantity
In this case, the quantity is given as 2000 - 100p. Substituting this into the formula, we get:
R(p) = p * (2000 - 100p)
Now, let's simplify this equation:
R(p) = 2000p - 100p^2
So, the polynomial that represents the total revenue when the shirts are p dollars each is R(p) = 2000p - 100p^2.
To find R(5), R(10), and R(20), we substitute the values of p into the polynomial equation:
R(5) = 2000(5) - 100(5)^2 = 10,000 - 2500 = 7,500
R(10) = 2000(10) - 100(10)^2 = 20,000 - 10,000 = 10,000
R(20) = 2000(20) - 100(20)^2 = 40,000 - 40,000 = 0
Therefore, R(5) = 7,500, R(10) = 10,000, and R(20) = 0.