Sansa collects Hummel figurines and Barbie dolls. Let H and B designate the number of pieces in each collection, respectively. Her utility functionis U(H, B) = max{3H, B}. ("max{x,y}" refers to "taking the maximal numberamongst the parameters." For example, max{2, 4} = 4.) Sansa has $140 to spendon her collection. The Hummel figurines cost $5 each and Barbie dolls cost $2 each.

(a)Draw and label Sansa's indifference curves for U = 3 and U = 6 in the same graph. [4 marks]

(b) FindSansa'soptimal bundle, indicating the number of Hummel figurines andthe number ofBarbie dolls in this optimal bundle. [6 marks]