The NCAA is making plans for distributing tickets to the upcoming regional basketball championships. The up to 10,000 available seats will be divided between the media, the competing universities, and the general public. Media people are admitted free, but the NCAA receives

$45 per ticket from universities and $100 per ticket from the general public. At least 500 tickets must be reserved for the media, and at least half as many tickets should go to the competing universities as to the general public. Within these restrictions, the NCAA wishes to find the allocation that raises the most money. An optimization output appears in Table 6.9.

(a) Briefly explain how this problem can be modeled by the LP max 45x2 + 100x3 s.t. x1 + x2 + x3 … 10,000 x2 - 12 x3 Ú 0 x1 Ú 500 x1, x2, x3 Ú 0

(b) through

(d) as in Exercise 6-1.