Economics question

AM has the following utility function: U(x, y) = 4y + x04. Let px and py be the corresponding prices and I her income. a) Setup the Lagrangian function and find the first order conditions (FOCs). Use these FOCs to find the expression for the marginal rate of substitution (MRS). What do you think is special about this indifference curve? D) Find the demand functions for x and y. c) Suppose AM lives in a city where px = 1, py = 32 and her job offers her / = 10. Find the optimal consumption. Now suppose she is offered a new job that offers her an income of 15 (1 = 15) but the job is in another city with px =2, py = 32. Should she take the job? Answer by comparing the utilities