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In the previous video,
we introduced the concept

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of price-per-click and
click-through-rate.

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Once we know both
of these quantities,

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we can calculate the
average price per display.

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This is simply
the average amount

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that an advertiser pays when
a user is shown their ad.

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We can compute this by
multiplying the price-per-click

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with the click-through-rate.

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Let's go through an example
to see how this works.

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Suppose we have 10 users who
search for "best LTE network".

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Google decides to display
Verizon's ad to all of them.

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We know that the
click-through-rate for Verizon

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and for the "best LTE network"
query is 0.2, so only two users

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click on the ad.

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Verizon must now pay
the price-per-click

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for each of these users.

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Since there were two clicks
and each click costs $25,

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Verizon must pay a
total of $50 to Google.

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If we consider how much Verizon
paid to Google on average,

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per user, or equivalently how
much Verizon paid per display

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of the ad, we just
divide the total amount

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of $50 for the 10
users who saw the ad.

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Doing this, we see that the
average price per display

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was $5.

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We could have obtained this
amount in a simpler way.

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In particular, as we defined
in the previous slide,

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this turns out to be exactly
the same as the price-per-click

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multiplied by the
click-through-rate.

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For our data then, to obtain
the average price per display

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we simply need to multiply
the price-per-click table

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and the click-through-rate
tables together.

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The last piece of
data that we need

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before we can define
our problem is

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we need to know how
popular the queries are.

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Obviously, Google does
not control how many times

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a search query will be
searched because the users are

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the ones who submit the queries.

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However, Google does
have an estimate

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of the number of
times, on average,

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the query will be
requested over a given day.

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For the example that we
have been building so far,

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let's suppose that we expect
to see "4G LTE" 140 times,

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"largest LTE" 80 times, and
"best LTE network" 80 times,

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as well.

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We're now ready to start
modeling this problem.

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The problem that we
will consider is this.

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How many times should Google
display each ad for each query,

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so as to maximize
their total revenue?

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In the next video,
we will formulate

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this as a linear
optimization problem.