Consider a consumer with the following preferences: U(x,y) = 20logx+y subject to 10x+10y=100 1) Write the consumer maximization problem, with all...

Consider a consumer with the following preferences:

U(x,y) = 20logx+y subject to 10x+10y=100

1) Write the consumer maximization problem, with all constraints.

2) Construct the Lagrangian, and solve for the optimal choices of x and y. Verify that you have included the appropriate constraints.

* I first solved it without knowing that if I just solve the equation, I get x=20 which does not adhere to the budget constraints (if you put x=20 to the budget constraints, you get 200+10y which is already bigger than 100.) Please help.