Question: The Kelmer Performing Arts Center offers a series of four programs that includes jazz, bluegrass, folk, classical, and comedy. The Program Coordinator needs to determine which acts to choose for next year's series. She assigned an "impact" rating to each artist that reflects how well the act meets the Center's mission and provides community value. This rating is on a scale from 1 to 4, with 4 being the greatest impact and 1 being the least impact. The theater has 500 seats with an average ticket price of $12. Based on an estimate of the potential sales, the revenue from each artist is calculated. The center has a budget of $20,000 and would like the total impact factor to be at least 12, reflecting an average impact per artist of at least 3. To avoid duplication of genres, at most one of artists 2, 7, and 9 may be chosen, and at most one of artists 3 and 6 may be chosen. Finally, the center wishes to maximize its revenue. Data are shown below.
Develop and solve an optimization model to find the best program schedule to maximize the total profit.

Dannenfelser Design works with clients in three major project categories: architecture, interior design, and combined. Each type of project requires an estimated number of hours for different categories of employees, as shown in the following table.

In the coming planning period, 184 hours of principal time, 414 hours of senior designer time, 588 hours of drafter time, and 72 hours of administrator time are available. Revenue per project averages $12,900 for architecture, $11,110 for interior design, and $18,780 for combined projects. The firm would like to work on at least one of each type of project for exposure among clients. Assuming that the firm has more demand than they can possibly handle, find the best mix of projects to maximize profit.