In addition to these production costs, each movie will have a $1 million advertising budget, which will increase to $3 million if the movie is to have a "big star" cast. Assume that the studio receives 80% of a film's gross receipts. The company would like to maximize its net profit (gross profit - production costs - advertising costs) for the year. Pentagonal has a production budget of $100 million and an advertising budget of $15 million. In addition, it would like to adhere to the following restrictions: a. At least half of the films produced should have a rating of PG or PG-13. b. At least two comedies are to be produced. If The Crush is produced, Bombs Away will not be. At least one drama is to be produced. At least two films should have big name stars. At least two PG films should be produced. At least one action movie with a big-name cast should be produced. On the next page, develop the linear programming model for this problem. Make sure you are clear about what your objective function is and what your constraints are. Finally, for the movies, you should remember that the no-name movie and the big star cast movies are different, so you have 20 decision variables, but you cannot produce two versions of the same film. (65 points)