Reducing Independent Set to a problem to prove that it is NP complete Given:


A set of available customers $c_1, c_2, \dots, c_n$.
A set of available foods $f_1, f_2, \dots, f_m$.
Each customer will choose a subset of the available food.


Problem:


Find the maximum number of customers that can be chosen, such that no two customers share the same food.


Question:


How to reduce the independent set problem to this problem, in order to prove that this is an NP-Complete problem ?
Hint: try to reduce each vertex to a customer and each edge to an available food.