# Q#4: First or Third Class Mailers?

Suppose you’re trying to optimize a mailing campaign where physical mail is sent to potential customers. There are two options to send advertising mail: either first class or third class. First-class costs \$0.50 per parcel with a delivery rate of 99% and third-class costs \$0.35 per parcel with a delivery rate of 65%. Third-class mail also receives a volume discount, if a batch of parcels is greater than 500, for first 500 are \$0.35 and anything additional costs \$0.32 per parcel.

Questions:

1. Assume our goal is to reach as many people with a cap of \$1000, which option would be the best?
2. Assume our goal is to reach 100 people, what option is best?

## Try it yourself

This is a statistics question and relies on your ability to calculate expected returns.

Let’s break down question 1 first with \$1000 dollars using 1st class mail, I would expect to reach the following number of people:

`1000/\$0.5*.99 = 1980 people`

Similarly we can calculate the number of people reached with the third class mail (a little more careful on the math):

`First 500: 500*.65 = 325 people reached1000 - 500*\$0.35 = \$825 left over825/\$0.32*.65 = 1675 peopleTotal = 325 + 1675 = 2000 people reached`

Now we clearly see that if our goal is to target the most number of people with the same budget, using third class mail is the better option.

For question two, we now have to consider how much it would cost to reach a certain number of people using either first or third class mail. It is still an expected value question.

For first class mail:

`100people/.99*\$.50 = \$50.50`

For third class mail:

`100people/.65*\$.35 = \$53.90`

Here we see that first class mail is the better option if we want to reach a target number of people under the bulk discount value.

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