Question 1 Consider the minimal cost for obtaining a specified level of utility problem between two goods, Goodx and Goody. Let x be the quantity of Good* whose price is $13 per unit and y be the quantity of Goody whose price is $15 per unit. The associated cost is therefore C(x, y) = 13x + 15y The targeted utility value is 178.4 where the utility function is given by U(x,y) = y(x + 1) (a) Solve the problem to minimise the cost, constrained by the desired utility level using Lagrange Multipliers. (b) Show that the solution found does actually minimise the cost function (amongst feasible x and y choices). (c) Calculate the optimal values for x*, and C* (d) Consider now the dual optimisation problem of maximisin the utility for the same money spent (cost) as calculated in part (c). Relate the optimal value of this problem to found in part (c).