I have the following problem:
I want to sell five computers. Denote them by $1, 2, 3, 4, 5$. I am allowed to take offers for subsets of the five computers. Three buyers, $A$, $B$, and $C$, want to make an offer. Each buyer has identified a maximum price that they would be willing to pay for various combinations: each individual buyer would only buy at most one parcel combination.
What is a possible linear programming formulation if I want to maximize the money that I make?
I would appreciate any help in approaching this problem.
Here are a few hints.
Define a binary variable for each combination. The objective is to maximize revenue. Two sets of constraints: don't sell the same computer more than once, and don't sell more than one combination to the same buyer.