Please help with this questionThis is my last question so please help with all!

(4 points) Use the following steps to find nonnegative numbers x and y that satisfy the following requirements: x + y = 48 and P = x2 y is maximized. a) Solve x + y = 48 for y. y = b) Substitute the result from a) into P = x2y, the equation for the variable that is to be maximized. P = c) Find the domain of the function P from part b), keeping in mind the given requirements. Domain is [ d) Find the derivative d P/dx, and solve the equation d P/dx = 0. dp dx which is equal to 0 when x = (If there are multiple solutions, enter them as 5, 6, 8.) e) Evaluate P at any solutions found in part d) as well as at the endpoints of the domain found in part c). f) State the conclusion: the maximum value of P is attained when x = and y = (2 points) An open box will be made by cutting a square from each corner of a 8 ft by 15 ft piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume? (Hint: draw a diagram. )