There are two goods: compact discs (C) and televisions (T).The utility function representing the two goods is U = C^0.7T^0.3.The price of compact discs (P_c) = 10/unit.The price of televisions (P_T) = 300/unit.Total income = $1000.

1. What is the optimal consumption bundle? What is the maximum level of utility? Don't use Langrangian.
2. Now solve for the optimal consumption bundle and maximum level of utility using the Lagrangian. Find and interpret .