Case interview #1: Mail sending

Question

Gaurav · Accepted Answer

I'm sorry if i understood the question wrong. But wont the option 2 better in every scenario? It costs the company 40c to send the mail with 90% accuracy. So to have the same reach to number of people as of option 1 (say we want 100 people to get the mail), we just need to send the mail to 111.11 people in option 2. With 90%, it will reach 100 people and will cost $44.44 whereas it will cost $50 with option 1. It will not matter if  only the accuracy rate was 80% in option 2.

ssss · Answer

there should have two utility functions, one for number of people received mail, one for the money spend:
U1=g(X) - f(0.5X);  U3=g(0.9X) - f(0.4X).    if money is the most important constraint, function f would be a very steep function, thus U3 > U1; if people is the most important, g would be a very steep function, thus U1 > U3. if we have g and f defined, we can set U1=U3,

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