Notes

I'll start with a simple
formula for this and that is that
revenue is equal to the number of things
you sell so the number sold times the
price of whatever it is so that's that's
revenue at its hair of course it gets
way more complicated than that
but you know it is what it is so what we
had here is a situation where we want to
create two linear equations so one for
the number of tickets sold the other one
for the price of the ticket so if he
looks here it says he'll sell 50 tickets
to be charged 30 bucks so he starts with
50 tickets so for every $1 price
increase or decrease he sells five more
tickets so let's first of all let's say
n is the number of $1.00 price decreases
so for example if he drops his price
down to $29.50 going to match that
situation so the linear equation that
I'm asked that situation is going to be
50 plus 5 and so let's for example he if
he drops the price $1 so n is 1 then he
has 55 people going he drops a 2 down to
28 bucks then he has 60 so 5 times 2 10
plus 50 is 60 so the price that he has
we starts with 30 and he decreases it $1
each time so it's going to be 30 minus n
so if n is 1 is 29 if n is to 28 so on
and so forth so this is my quadratic
equation right here so that is the
quadratic equation now it's not in the
form that we would like it to be in we
would like it to be in you know ax
squared plus BX plus plus BX that's not
an excess 2 plus BX plus C that's the
form that we would like it to be in so
all we have to do is foil this out so
let's go ahead and do it so 50 times so
first outside inside last 50 times 30 so
that's 150 so 150 first outside so
that's negative 50 in inside 150
actually it should be 1500 shouldn't it
to zeros 150 n and then minus 5 and square
now just rearrange and do the mapping we
put the N squared first negative 5n
squared that's going to be plus 150 N
and then plus 1500 so I just combined my
two middle terms there and you know as
simple as that 5 times 30 and soon quick
check on my mental math and want to mess
this up here on video alright so there
it is so that's my revenue equation so
what I need to do now is just do quick
mental check this is a maximum question
see Max's revenue so that tells me I
need to find a vertex so excuse me so in
order to find the vertex I want to use
the formula X is equal to negative B
over 2a and in my case n is equal to
negative B over 2a so and B number of
price increases so n is equal to
negative 100 divided by 2 times negative
5 and that's going to leave me with
negative 100 divided by negative 10
which is 10 so he's going to have to
make 10 price decreases I kept keep
saying increases so 10 price decreases
so basically its price is going to be so
I'll go back to my price equation which
is 30 minus n so 30 minus 10 which is 20
so I want to find the revenue or sorry
the number sold the number sold would be
550 plus 5 times 10 so he's going to
sell 100 tickets now and then his
revenue if I wanted to find it I have
two options i have two options i can
take this 10 and go back or this 10 and
go back in here sub in here and that
gives you a revenue really my vertex for
this situation is the number of price
increases and the revenue and our but
again I don't have to do that I can just
go 20 times 1,000 that's going to give
me 20,000 so that's how much money is
going to make so I should be in the boat
tour business that's a math making the
video business