Consumer Choice Model: Suppose you have a budget of $116

Consumer Choice Model: Suppose you have a budget of $116 to spend of pretzels and beer. Your utility function is U = 30p + 36b+ 2pb – 0.5p2 – 0.5b2. The price of a small bag of pretzels is $2, and the price of a pint of beer is $4.

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 pretzels and beer? Does the Utility-Maximizing Rule hold? i.e. MUp/Pp = MUB/PB. (Show your work).