I used a logistic regression to build a model to score the value of each customer. Now suppose we have scored 10K customers and plan to run a marketing campaign on them. Two pilot programs had been conducted and the outcomes are summarized below.
Program 1:
Spent $.40 on each customer of first 1K customers. Got 10 purchases and $.45/customer profit.
Spent $.30 on each customer of next 3K customers. Got 20 purchases and $.28/customer profit.
Spent $.20 on each customer of next 5K customers. Got 40 purchases and $.22/customer profit.
Spent $.10 on each customer of next 2K customers. Got 10 purchases and $.12/customer profit.
Program 2:
Spent $.40 on each customer of first 1K customers. Got 10 purchases and $.45/customer profit.
Spent $.30 on each customer of next 2K customers. Got 10 purchases and $.32/customer profit.
Spent $.20 on each customer of next 7K customers. Got 50 purchases and $.20/customer profit.
Spent $.10 on each customer of next 1K customers. Got 5 purchases and $.09/customer profit.
Based on these 2 pilot program outcomes, I would like to see the optimal allocation of marketing spend to maximize the purchases and profit. That each, how many customers need to allocate to spend $.4 group, how many to spend $.3 group. I don't know which math/statistics methods I should use to solve this problem.
