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, such as woodworking, word processing, and car maintenance; and humanistic, such as history, music, and fine arts. 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.

(a) Devise an optimal course offering for the college.

(b) Show that the dual price of an additional course is $1500, which is the same as the revenue per practical course. What does this result mean in terms of offering additional courses?

(c) How many more courses can be offered while guaranteeing that each will contribute $1500 to the total revenue?

(d) Determine the change in revenue resulting from increasing the minimum requirement of humanistics by one course.