Please thoroughly and briefly explain all parts of the answer!

1. (35 points). Bennett uses nuts (denoted by N) and bolts (denoted by B) to keep things together. Each bolt requires one nut, so Bennett's utility function is U(N,B) = min{N,B}. The price ofa nut is $1, While the price ofa bolt is $2. Bennett has 120 nuts. a) Find Bennett's optimal consumption bundle. If you can remember the demand functions, then you do not need to derive them. How large is his net demand for nuts and bolts, respectively. b) The things that Bennett needs to keep together are starting to fall apart. He now realizes that each bolt requires not one, but two, nuts. This changes Bennett's preferences. What is his new utility function? c) Given his new, more nuts-intensive preferences, nd Bennett's optimal consumption bundle. If you can remember the demand functions, then you do not need to derive them. How large is his net demand for nuts and bolts, respectively