Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16 dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B ^1/2 + 4Z ^1/2

1. Write her budget constraint.

2. Set up the Lagrangian and find her optimal consumption.

3. What is her new consumption if the price of burgers becomes 16 dollars?