A college department must plan the course offerings for the next semester. The education plan requires that at least 20 core courses and 20 electives be offered.

Regardless of core or elective, a total of at least 60 courses must be offered. Each core course counts for 3 units, and each elective counts for 4 units. The program also requires that at least 205 units be offered.

The cost of teaching a core course is $2,600 in terms of faculty salary, and the cost of teaching an elective is $3,000. The goal of the department is to meet the education plan requirement while minimizing the cost of hiring faculty.

1. 1)  Formulate the LP problem.
2. 2)  Provide the graphical solution to this problem.
3. 3)  At the optimal solution, which constraint is not binding, what is the value of the slack or surplus? Provide an economic interpretation of the slack or surplus value.