1. Mathematics
2. Linear Transformation
3. Linear Programming
4. 4043

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How would I turn this real world problem into a linear programming problem?

The licensing capacity of a preschool is 50, which is the constraint. Initially all children attended full time. The changes incorporated were the creation of three different enrollment positions for children to attend our school. One is the normal full-time (5 days a week @ $650.00 per month), but in addition a part-time slot of (3 days a week Monday, Wednesday, & Friday @ 460.00 per month) and a (2 day a week Tuesday & Thursday @ 350.00 per month).

The 50 full time only slots net us an income of $32,500.00 per month, but the replacement of the varying schedules increase the income dramatically. For example daily attendance per month of 30 children @ 650 = $19,500. 20 children @460 = $9,200. And 20 children @350 = 7,000. Our limit is still 50 children daily, but this combination netted us $35,700 per month. This is a $3,200 increase every month, which amounts to an additional $38,400.00 per year.