00:01
So we have a total of 53 rooms in our hotel, and the room rate is 98 per room for a single, or it is gonna be 98 minus 3 times x minus 1 per room for groups of size x.
00:38
And room for a single room, because if we have two rooms, then you would subtract just $3.
00:51
So, okay.
00:52
So then your total group income for a group of x is equal to, well you're renting out x rooms, times the room rate, which is 98 minus 3x plus 3, distributing that negative 3 to the negative 1, so this then is 98, no it's 101, x minus 3x squared.
01:32
And what is the most money you can make from rental to a single group? well, that means if we call this f of x, then we want to find the max value for x, or the max value for f of x.
01:53
And this is a parabola, so it's gonna be at the vertex, if we write this in vertex form, so let's do that.
02:05
We have f of x is negative 3x squared plus 101x.
02:13
Well that is negative 3 times x squared plus 101 divided by 3x...