1. (20 points) Consider the following utility function for cans of beer (B) and slices of pizza (Z) for Lisa:

U (B,Z) = ln B + 2 ln Z

MU_B = 1/B

MU_Z = 2/Z

Assume that a can of beer costs $1 and a slice of pizza costs $3

a. (5 points) Suppose Lisa has a wealth level of $90. What quantity of beer and pizza should Lisa purchase?

b. (5 points) Provide a function describing how much beer and pizza Lisa should purchase for any wealth level w. In other words, I want you to provide two functions, B(w) and Z(w), that tell me how many cans of beer and slices of pizza she purchases for each possible level of wealth.

c. (10 points) Now assume the pizza parlor only sells whole pizza pies - in other words, individual slices are not sold. Also, pizza pies can only be bought in whole number units. For example, you can buy 1 or 2 pizza pies, but not 1.67 pizza pies. If a pizza pie has 8 slices and costs $16 and cans of beer cost $1, how many pizza pies and cans of beer should Lisa purchase if she has a budget of $50?