The Bottles Film Festival draws thousands of people each year to view some of the latest motion pictures and award medals for the best. Planners are now selecting one of time slots t = 1,c, n for each of the j = 1,c, m films to be shown. From past experience, the festival can estimate numbers aj, j=!number of guests who would like to watch both film j and file j=. Now they wish to schedule the films so that no more than 4 are shown at any time and the minimum total number of guests are inconvenienced by two movies they would like to see being scheduled at the same hour.

(a) Explain why appropriate decision variables for a mathematical programming model of this problem are 1j = 1,c, m, t = 1,c, n2 xj, t ! e 1 if j occurs at t 0 otherwise

(b) Formulate an objective function to minimize the total number of guests inconvenienced by movies scheduled at the same time. (Hint: When xj, txj=, t = 1, films j and j= are scheduled at the same time t.)

(c) Formulate a system of m constraints assuring that each film is scheduled at some time.

(d) Formulate a system of n constraints assuring that no more than 4 movies are schedule at any time.

(e) Complete your model with an appropriate system of variable-type constraints.

(f) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.

(g) Code your model in AMPL (paralleling Tables 2.6 and 2.7).