The utility function of Joy is (, ) = + 100 - ², where B is the number of bells and C is the number of shells it can place in its garden.Her garden is 500 square meters, each bell needs one square meter to be placed and each shell needs 4 square meters to be placed.He can get both for free.

a)How many bells and how many shells should it use to maximize its usefulness?

b)If her garden grows by 100 square meters how many bells and how many shells should she use to maximize its usefulness?

c)If her garden was 144 square meters how many bells and how many shells should she use to maximize its usefulness?

d)If she wants to use bells and shells, how many square meters should her garden be at least?