(a) The Physics Club should charge $11 per T shirt to maximize revenue. At this price, the total revenue is given by R = pq = p(2p² + 33p) = 11(2(11)² + 33(11)) = $1,331.

(b) P = Revenue Cost

= pq (100 + 8q)
= p(2p² + 33p) (100 + 8(2p² + 33p))
= 2p³ + 49p² 264p 100

The lower price corresponds to a local minimum for the function P, while the higher price gives a maximum. Therefore, p = $12.93 $13.

(c) With this price, the profit is P(13) = $355 per day.