5. A person's preferences over brands of shampoo (P stands for Pert; D stands for Dove) are represented by U = P + 1.2D a. Suppose that Pert sells for $3 for a 32-ounce bottle, and Dove sells for $4 per 32 ounce bottle: Pp = 3; Pcl = 4. Suppose he plans to spend $12 this year on shampoo. How should he optimally spend his money? b. Suppose now that the price of Port remains $3, but Dove lowers its price to $3. Now how should our person optimally spend his $12? 0. One day, our consumer walks into a store where he is offered a free bottle of either Pert or Dove(not both). Given his preferences, which one will he choose