In class we discussed utility maximization forf consumers and cost minimization for firms. Here we consider cost minimization for consumers. Consider the problem min pxX + pyY such that U(X; Y ) = : The consumer minimizes the cost of buying goods X and Y such that utility is equal to . a) Sketch a diagram that illustrates the objective, constraint, and optimal choice of X and Y b) Let px = 1, py = 1 and U(X; Y ) = XaYa. Find the optimal quantities for X and Y . c) How much money does the consumer spend to purchase these optimal quantities