Suppose that the consumer's utility function is given by u(c_{1 ,}c₂) = c₁^.50 c₂^.50 . Using a Lagrangian, solve algebraically for the consumer's optimal choice of c₁ and c₂ as functions of P1, P2, t2, and Y . Graphically show how, for this particular utility function, the optimal choice changes due to the imposition of the sales tax on good 2.