Robby is a teenager. Suppose that Robby's preferences are represented by the following utility function: = 2 + 8 where x and y are, respectively, the amounts of nutritious food and junk food Robby consumes per day. Assume that Robby has $12 to spend on food every day; the price of nutritious food is $4 per unit and the price of one unit of junk food is $1.

Find the optimal consumption bundle chosen by Robby. Given that he cannot consume negative amounts of any good, how many units of the two types of food will he consume every day? Illustrate your answer on the graph of part a by including the indifference curve that Robby attains at his optimal point.