Mary's utility function is U(b, c) = b + 100c c2, where b is the number of silver bells in her garden and c is the number of cockle shells. She has 500 square feet in her garden to allocate between silver bells and cockle shells. Silver bells each take up 1 square foot and cockle shells each take up 4 square feet. She gets both kinds of seeds for free.

(a) To maximize her utility, given the size of her garden, Mary should plant ..... silver bells and ..... cockle shells. (Hint: Write down her "budget constraint" for space. Solve the problem as if it were an ordinary demand problem.)

(b) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells? ....... silver bells. How much should she increase her planting of cockle shells? ........

(c) If Mary had only 144 square feet in her garden, how many cockle shells would she grow? .......

(d) If Mary grows both silver bells and cockle shells, then we know that the number of square feet in her garden must be greater than