On a given day, John enjoys the consumption of croissants

(c) and butter

(b) according to the function U

(c,

b) = 20c − c2 + 18b − 3b2.

How many croissants and portions of butter does he consume during a day? (Assuming John does not face any budgetary constraints.)

John has been advised to restrict the total consumption of croissants and butter consumed to 5. How many croissants and portions of butter will he consume under these circumstances?

Peter enjoys two products x and y according to the utility function U(x, y

) = "x2 + y2.

Maximise Peter’s utility if px = €3, py = €4, and he has €50 to spend.

Construct a graph to illustrate Peter’s indifference curve and its point of tangency with his budget constraint. What does the graph imply about Peter’s choice?