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2. Cobb Douglas utility function: U = 10C 0:2M0:8 , budget equation is: C + 2M = 50. Use the Lagrangian method to solve for C and M (a) Write out the maximization problem (i.e., choose blank and blank to maximize blank subject to blank. (b) Write out the Lagrangian function. (c) Derive First Order Condition (FOC) 1, @L @C = 0: (d) Derive FOC 2, @L @M = 0: (e) Derive FOC 3, @L @ = 0: (f) Divide FOC 1 by FOC 2 to obtain the tangency condition: (g) Substitute the tangency condition into FOC 3 to calculate C* or M* (your choice).