Suppose that a consumer has a choice between gallon jugs of milk and half-gallon jugs of milk. The consumer only cares about how much milk she consumes and does not care about the size of the jug.
a. Write a utility function for this consumer.
b. Suppose the price of a half-gallon jug of milk is $2, the price of a gallon jug of milk is $5, and the consumer has $10 to spend on milk. Set up a Lagrangian and derive the first order conditions for the maximization problem.