Question 1 Consider the minimal cost for obtaining a specified level of utility problem between two goods, Good, and Goody. Let x be the quantity of Good, whose price is $13 per unit and y be the quantity of Good, 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*, y*,* and C* (d) Consider now the dual optimisation problem of maximising the utility for the same money spent (cost) as calculated in part (c). Relate the optimal ** value of this problem to 1* found in part (c).