John's utility function is given by the following equation

(, ) = min(3, 4),

where x is the unit of good X consumed, and y is the unit of good Y consumed. John's budget is $240, price of good X (x) is $6, and price of good Y(y )is $4. Show all the steps, with definition of every new notation used in the steps.

a)What is John's optimal consumption(* , * )? Graph the optimal consumption along with appropriate budget line and indifference curve.

b)Ifxincreases from $6 to $8, what is the new optimal consumption(F , F )? Graph the new optimal consumption along with appropriate budget line and indifference curve on part a)'s graph.

c) Ifxincreases from $6 to $8 what is the substitution effect and income effect in terms of good X?