Matt consumes only bagels and coffee. Her utility function is U = BC where B is the number of bagels consumed daily and coffee is the number of cups of coffee consumed daily.

a) Would Matt prefer to consume 2 bagels and 3 cups of coffee or would she prefer to consume 3 bagels and 2 cups of coffee?

b) Suppose matt has consumed 2 bagels and 3 cups of coffee today. How much additional utility will she get from eating an additional bagel?

c) What is his marginal rate of substitution of bagels for coffee?

d) If Matt plans to consume 4 bagels and 3 cups of coffee today, how many cups of coffee would you have to give him to convince him to give up one of the bagels?

e) Matt has a budget of $16. If bagels cost $2 each and coffee costs $4 per cup, what is Matt's utility-maximizing quantity of each good?