Developing a mathematical programming model to maximize the total costs

MTM produces motion pictures in Texas and distributes them nationwide. Currently, it is considering ten possible films.  These include dramas, comedies, and action adventures. The success of each film depends somewhat on both the strength of the subject matter and the appeal of the cast. Estimating the cost of a film and its potential box office draw is inexact at best. However, the studio must rely on its experts' opinions to help it evaluate which projects to undertake. Table below lists the films currently under consideration, their rating, type, cost and cast information.

Table:

In addition to these production costs, each move will have a $1million advertising budget, which will increase to $3 million if the move is to have a big star case.  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.  MTM 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:

1. At least half the films produced should have a rating of PG or PG-13.

2. At least two comedies are to be produced.

3. If The Crash is produced, Bombs Away will not be.

4. At least one drama is to be produced.

5. At least two films should have big-name casts.

6. At least two PG films should be produced.

7. At least one action move with a big-name cast should be produced.

Develop a mathematical programming model and solve.  Discuss your results [total profits, total costs, etc].