operations research assignment problem

(points: 15) Santa Claus has n gifts that he plans to distribute among m kids. Each kid i has a happiness-value gij for gift j which is known to Santa (of course, Santa knows!). The happiness of kid i is the sum of the happiness-values of the gifts that he/she receives. Santa's goal is to distribute the gifts in such a way that the total happiness over all kids are maximized. (a) (points: 10) Formulate an optimization model for Santa. Interpret the meaning of your decision variables, objective function, and constraints. (b) (points: 5) If Santa's goal changes to make the least happy kid as happy as possible, modify the objective function in your above model accordingly. Then linearize your objective function. Hint: 1. Consider this as a variant of the assignment problem that one gift can be distributed to only one kid, but one kid can receive multiple gifts. 2. To gain some understanding, consider writing a formulation for the following example instance where n=6,m=4 and the happiness-values are as shown below