Problem # $4$

The Continuing Education Division at the Ozark Community College offers a total of $30$ courses each semester. The courses offered are usually of two types: practical and humanistic. To satisfy the demands of the community, at least $10$ courses of each type must be offered each semester. The division estimates that the revenues of offering practical and humanistic courses are approximately $$1500$ and $$1000$ per course, respectively.

Develop an optimization model that can be used to find the optimal course offering plan.