我可以在这种情况下使用线性编程吗？ 如何使用scipy.optimize.linprog进行设置？

Question

Let's say I have to come up with a solution to fill each role needed to run an office, and maximize productivity. There are several roles (office manager, front desk person, manager, etc). Each role has several candidates. Each candidate has a salary, and some number to represent their work productivity. Now if I have 20,000 a month budget, I need to maximize the work productivity while staying under budget. To me this seems like a pretty basic example of a linear programming problem, however I am getting stuck on the fact that I have multiple candidates for each position. The examples I found are usually static options, such as having an apple, orange, and banana and maximizing production of food under some constraints. My scenario would be more like choosing a green fruit, red fruit, and yellow fruit where there are many of each.

If I have 3 positions total for the office, I believe the basics of my problem would be something like this:

maximize: x[prod] + y[prod] + z[prod]

x[sal] + y[sal] + z[sal] <= 20,000

x, y, and z positions must all be filled.

Where do I go from here? I'm new to linear programming so please correct me if anything doesn't make sense.

Answer 1

This is not a linear programming problem. Since you can't hire half a worker, this is an integer programming problem, making it much harder. scipy.optimize.linprog doesn't handle integer programming. You'd have to get a different solver.