Please provide correct solution and working-out. Greatly Appreciated!!! Question 1Consider the budget constrained utility maximisation problem between two goods,Good, and Goody.Let x be the quantity of Good, whose price is $13 per unit andy be the quantity of Good, whose price is $15 per unitThe total budget is $560. (Therefore, the budget constraint is 13x + 15yThe Utility function is given by U(x, y)= x(y + 1)=560).(a) Solve the problem to maximise the utility, constrained by the budget using LagrangeMultipliers.(b) Show that the solution found does actually maximise the utility function (amongstfeasible x and y choices).(c) Calculate the optimal values for x*, y*, λ* and U*(d) Consider now the dual optimisation problem of minimising the cost (Budget, B(x, y))to achieve the utility U* as calculated in (c). Relate the optimal values of this problemto those found in (c) and also B*.

To solve the problem using Lagrange multipliers, we set up the following Lagrangian function:L(x, y,…

Question 1 Consider the budget constrained utility maximisation 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 total budget is $560. (Therefore, the budget constraint is 13x + 15y = 560). The Utility function is given by U(x, y) = x(y + 1) (a) Solve the problem to maximise the utility, constrained by the budget using Lagrange Multipliers. (b) Show that the solution found does actually maximise the utility function (amongst feasible x and y choices). (c) Calculate the optimal values for x*,y*, λ* and U* (d) Consider now the dual optimisation problem of minimising the cost (Budget, B(x, y)) to achieve the utility U* as calculated in (c). Relate the optimal values of this problem to those found in (c) and also B*.