Could you please help me solve the below question:

Question 3. (35 points) Consider the following optimization problem: maxU = U(x, y) subject to Prl + Pyy = B where Pr,Py and B are constants. (i) (4 points) Write the Lagrangian and write the first order conditions for the La- grangian. (ii) (12 points) Now assume that U(x, y) = x2 + y, Px = 2, Py = 4 and B = 100. Use both Gaussian elimination and Cramer's rule to find A* along with the optimal levels of x* and y*. Calculate U*. (ii) (9 points) Using the Bordered Hessian matrix, verify that the second-order con- ditions for a maximum or minimum are satisfied. (iv) (10 points) Suppose all parameters are the same as (ii) except B changes from 100 to 101. Based on result in (ii), use )* to obtain the estimated value of the new maximized value of utility