3. Suppose that a consumer has a choice between gallon jugs of milk and half-gallon jugs of milk. The con-sumer 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.c. Is there a solution to the first-order conditions? If so, solve for the optimal quantities of gallon jugs and half-gallon jugs. If not, what is the solution to the maximization problem?
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