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# Maximize Retrun

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.