# Yuma 4×4

##### Media and Communications In the previous video,
we introduced the concept of price-per-click and
click-through-rate. Once we know both
of these quantities, we can calculate the
average price per display. This is simply
the average amount that an advertiser pays when
a user is shown their ad. We can compute this by
multiplying the price-per-click with the click-through-rate. Let’s go through an example
to see how this works. Suppose we have 10 users who
search for “best LTE network”. Google decides to display
Verizon’s ad to all of them. We know that the
click-through-rate for Verizon and for the “best LTE network”
query is 0.2, so only two users click on the ad. Verizon must now pay
the price-per-click for each of these users. Since there were two clicks
and each click costs \$25, Verizon must pay a
total of \$50 to Google. If we consider how much Verizon
paid to Google on average, per user, or equivalently how
much Verizon paid per display of the ad, we just
divide the total amount of \$50 for the 10
users who saw the ad. Doing this, we see that the
average price per display was \$5. We could have obtained this
amount in a simpler way. In particular, as we defined
in the previous slide, this turns out to be exactly
the same as the price-per-click multiplied by the
click-through-rate. For our data then, to obtain
the average price per display we simply need to multiply
the price-per-click table and the click-through-rate
tables together. The last piece of
data that we need before we can define
our problem is we need to know how
popular the queries are. Obviously, Google does
not control how many times a search query will be
searched because the users are the ones who submit the queries. However, Google does
have an estimate of the number of
times, on average, the query will be
requested over a given day. For the example that we
have been building so far, let’s suppose that we expect
to see “4G LTE” 140 times, “largest LTE” 80 times, and
“best LTE network” 80 times, as well. We’re now ready to start
modeling this problem. The problem that we
will consider is this. How many times should Google
display each ad for each query, so as to maximize
their total revenue? In the next video,
we will formulate this as a linear
optimization problem.