Benny consumes coffee (c) and bagels (b). He has an income of 42. Bagels are sold in an unusual way. There is only one supplier and the more bagels Benny buys, the higher the price per unit. In fact, bagels cost Benny a total of 2b2 for b bagels.1 Coffee is sold normally at a price of $2 per unit. Benny's utility function is u(b, c) = 12b + 4c.

(a) (5 points) Write out Benny's budget constraint.

(b) (5 points) Depict Benny's budget line on a graph. Also draw a few of Benny's indiffer- ence curves.

(c) (10 points) Find the optimal bundle for Benny.