1) 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 not about the size of the jugs of milk.

a. Write a utility function for this consumer.

b. Suppose the price of the half gallon jug of milk is $2, the price of a gallon jug of milk is $5, and the consumer has only $10 dollars to spend on milk. Set up a Lagrangian and set up the first order conditions for the maximization problem.

c. Is there a solution to the first order conditions? If so,solve for the opitmal quantities of gallon jugs and half gallon jugs. If not, what is a solution to the maximization problem?