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.
(b) If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of 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 _____.