A company wishes to put together an academic ''package'' for an executive training program. There are five area colleges, each offering courses in the six fields that the program is designed to touch upon.
The package consists of 10 courses; each of the six fields must be covered. The tuition (basic charge), assessed when at least one course is taken, at college i is Ti (independent of the number of courses taken). Moreover, each college imposes an additional charge (covering course materials, instructional aids, and so forth) for each course, the charge depending on the college and the field of instructions. Formulate an integer program that will provide the company with the minimum amount it must spend to meet the requirements of the program.