1. ## Purchasing and bundling data

This is a post by jonarnold85.

Originally Posted by jonarnold85
I'm hoping someone is able to help me fairly quickly here. This should be a very simple problem but for some reason I'm struggling with it. I'm trying to calculate what will be more profitable for my company. I'm looking for what formula I would need to run this calculation. My dilemma:

I'm purchasing data, but my request must go through with no typos. This data can be bought as a "bundle." I can either buy it individually by paying 0.35 dollars for package A and 1.75 dollars for package B for a total of 2.10 dollars. Or I can buy bundle C which has all the same data for just 1.75 dollars. While C sounds like the obvious option, C has limitations. When I buy packages A and B I can run package A first before ever paying for B. If the data in package A suggest that a typo was made, I do not have to buy package B. I can fix the typo and resubmit. Resubmitting will mean that I fix the data and buy packages A and B for a total of 2.10 dollars plus the 0.35 dollars I paid initially for package A, giving me a total of 2.45 dollars out of pocket. If I buy bundle C I pay 1.75 dollars. If a typo is made here I'm out 1.75 dollars plus I have to pay another 1.75 dollars to run it again for a total of 3.50 dollars.

I'm making the assumption that a typo will only be made once, never twice. What I want to be able to calculate is what percentage threshold of making a typo would justify purchasing the first option for 2.10 dollars vs the second option for 1.75 dollars. I can run a report to see what percentage of orders are submitted with a typo. I want to use this percentage to determine which one is more cost effective.

If this all sounds like gibberish please let me know, because it certainly felt like I was typing gibberish

2. ## Re: Purchasing and bundling data

Originally Posted by jonarnold85
I'm purchasing data, but my request must go through with no typos.

This data can be bought as a "bundle."

I can either buy it individually by paying
0.35 dollars for package A
1.75 dollars for package B

for a total of 2.10 dollars.

Or I can buy bundle C which has all the same data for just 1.75 dollars.

While C sounds like the obvious option, C has limitations.

When I buy packages A and B I can run package A first before ever paying for B.
If the data in package A suggest that a typo was made, I do not have to buy package B.
I can fix the typo and resubmit.
Resubmitting will mean that I fix the data and buy packages A and B for a total of 2.10 dollars plus the 0.35 dollars I paid initially for package A, giving me a total of 2.45 dollars out of pocket.

If I buy bundle C I pay 1.75 dollars. If a typo is made here I'm out 1.75 dollars plus I have to pay another 1.75 dollars to run it again for a total of 3.50 dollars.

I'm making the assumption that a typo will only be made once, never twice.
What I want to be able to calculate is what percentage threshold of making a typo would justify purchasing the first option for 2.10 dollars vs the second option for 1.75 dollars.

I can run a report to see what percentage of orders are submitted with a typo. I want to use this percentage to determine which one is more cost effective.
reposted for clarity

3. ## Re: Purchasing and bundling data

Originally Posted by jonarnold85
I'm purchasing data, but my request must go through with no typos.

This data can be bought as a "bundle."

I can either buy it individually by paying
0.35 dollars for package A
1.75 dollars for package B

for a total of 2.10 dollars.

Or I can buy bundle C which has all the same data for just 1.75 dollars.

While C sounds like the obvious option, C has limitations.

When I buy packages A and B I can run package A first before ever paying for B.
If the data in package A suggest that a typo was made, I do not have to buy package B.
I can fix the typo and resubmit.
Resubmitting will mean that I fix the data and buy packages A and B for a total of 2.10 dollars plus the 0.35 dollars I paid initially for package A, giving me a total of 2.45 dollars out of pocket.

If I buy bundle C I pay 1.75 dollars. If a typo is made here I'm out 1.75 dollars plus I have to pay another 1.75 dollars to run it again for a total of 3.50 dollars.

I'm making the assumption that a typo will only be made once, never twice.
What I want to be able to calculate is what percentage threshold of making a typo would justify purchasing the first option for 2.10 dollars vs the second option for 1.75 dollars.

I can run a report to see what percentage of orders are submitted with a typo. I want to use this percentage to determine which one is more cost effective.
let

$ab=2.10$

$aab=2.45$

$c = 1.75$

$cc = 3.50$

$p$ is the probability of a typo

$cost_{AB}=E[\text{cost using AB}] = \\ \\ p\cdot aab + (1-p)\cdot ab =\\ \\2.1 (1 - p) + 2.45 p=\\ \\2.1 + 0.35 p$

$cost_C=E[\text{cost using C}] =\\ \\ p \cdot cc + (1-p) \cdot c = \\ \\ 1.75 (1 - p) + 3.5 p=\\ \\ 1.75 + 1.75 p$

Solve $cost_{AB} < cost_C$ for $p$

I leave you to do the remaining algebra. I get $p>0.25$ justifies using package AB