A small college has space for a maximum of 1,000 students. The college can identify 500 of its students who are willing to pay $20,000 per year and 500 students who are willing to pay $10,000 per year. The college has annual fixed costs of $10 million, and the variable cost for each additional student is $5,000. To continue operating, the college must receive payments equal to its total costs (that is, total fixed costs + total variable costs).
If the college charges all students the same tuition, what tuition can it charge to cover all of its costs?