Two more optimization problems to work on.

1. Suppose my utility function for beer and nuts is given by U(B,N) = B^.6N^.3 , where B is the number of beers and N is the number of bowls of nuts consumed. Each beer costs $1 and each bowl of nuts costs fifty cents. I have $6 to spend. How many beers and how many bowls of nuts should I consume? What is my total utility?

2. USXYZ Corp., currently located in a unionized state, is considering relocation to South Carolina. The company manufactures specialty metal products, one of which sells for $800 per ton in a very competitive product market.

The union wage is $400 per week per worker and the weekly cost of capital is $300 per unit. The production function is estimated to be the following Cobb-Douglas function

Q = 10 K^.3L^.4, where

Q is weekly output, in tons,

L is the number of workers employed, and

K is the number of units of capital used per week.

Find the optimal expansion path of production by the company, optimal weekly output, and the company's weekly profits.