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.

I came up with the polynomial being:
R(p)= 2000-100p^2

b) Find R(5), R(10), and R(20).

Your math is ok, but your given data makes little sense.

e.g. at R(5) = 2000 - 100(25) = -500
he would be losing 500 dollars if he charges $5 per shirt

If he gave the shirts away (no charge for a shirt or R(0)), his revenue would be 2000 ????

Swimming space. The length of a rectangular swimming pool is 2x -1 meters, and the width is x + 2 meters. Write a polynomial a(x) that represents the area. Find A (5).

The length of a rectangular swimming pool is 2x -1 meters, and the width is x + 2 meters. Write a polynomial a(x) that represents the area. Find A (5).

To find the polynomial R(p) that represents the total revenue when the shirts are p dollars each, we need to determine the revenue generated by selling each shirt at price p, and then multiply it by the total number of shirts sold.

In this case, we know that the vendor expects to sell 2000 - 100p shirts at a tournament. We also know that the revenue generated by selling one shirt at price p is simply p.

Therefore, the polynomial representing the total revenue R(p) would be:

R(p) = p * (2000 - 100p)

Simplifying further:

R(p) = 2000p - 100p^2

Now, let's move on to part b, where we need to find R(5), R(10), and R(20):

To find R(5), substitute p = 5 into the polynomial:

R(5) = 2000(5) - 100(5)^2
= 10000 - 100(25)
= 10000 - 2500
= 7500

So, R(5) = 7500.

To find R(10), substitute p = 10 into the polynomial:

R(10) = 2000(10) - 100(10)^2
= 20000 - 100(100)
= 20000 - 10000
= 10000

So, R(10) = 10000.

To find R(20), substitute p = 20 into the polynomial:

R(20) = 2000(20) - 100(20)^2
= 40000 - 100(400)
= 40000 - 40000
= 0

So, R(20) = 0.