Using calculus set up a constrained optimization problem

Question

Consumer Choice Model:

Suppose you have a budget of $1,300 to spend of beer and pizza this year. Your utility function is U = 200B + 150P - 0.5B² - 0.25P². The price of a beer is $5 and the price of a pizza is $10.

a) Using calculus, set up a constrained optimization problem using the Lagrangian multiplier that derives the optimal consumption of pretzels and beer. Find the optimal values.

b) At the optimum, what are the marginal utilities of both pizza and beer? Does the Utility-Maximizing Rule hold? i.e. MU_p/P_p = MU_B/P_B. (Show your work).

c) Does the utility function indicate a relationship between pizza and beer?