nd Optimization Fall 2023 Question 3 of 5 This question: 1 point(s Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the indicated expression. Complete parts (a) through (f) below. x + y=280 and the product P = xy as large as possible. (a) Solve x + y = 280 for y (Type an equation.) (b) Substitute the result from part (a) into P =xy, the equation for the variable that is to be maximized. (Type an equation.) (c) Find the domain of P found in part (b) (Type your answer in interval notation.) dP (d) Find de Solve the equation dx dP dx and when dy =0, x =(Use a comma to separate answers as needed.) (e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c). To answer the first part, select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. There was one solution in part (d). For that solution, P = O B. There were two solutions in part (d) For the lesser value of x, P = For the greater value of x, P = Evaluate P at the endpoints of the domain. At the lower endpoint, P = At the upper endpoint, P =] (f) Give the maximum value of P, as well as the two numbers, x and y, whose product is that value. P =when x = _and y =