Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has four times the alcohol as a sixpack of beer. Assume that Tony only cares about the total amount of alcohol in his basket.(use vodka on X axis and beer measured in six pack on Y axis)

a)Devise a utility function to represent these preferences.

b)What is his marginal rate of substitution of a bottle of vodka for six packs of beer?

c)Suppose a bottle of vodka costs $45, a six pack of beer costs $15 and Tony has $180 budget. Write the budget constraint.

d)Solve Tony's utility maximization problem and find out optimal combination?

e)Now suppose that a bottle of vodka cost has increased to $60. What will be his new optimal combination?