4. Consider a consumer with the following preferences:
(x, y) = 20 logx+ 5
who face prices px = 10, py= 10, and has wealth w= 100.
(a) Write the consumer maximization problem, with all constraints.
(b) Construct the Lagrangian, and solve for the optimal choices of x and y
Verify that you have included the appropriate constraints.
(c) Find the demand curves for x and y