Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x + y = 78 and P =x2y is maximized a. Solve x+y=78 for y. y= 78-x b. Substitute the result from part a into the equation P = x2y for the variable that is to be maximized. mm (a) The function to be maximized is V(x) where x is the side length of the square. Find the formula of the function to be maximized. V(x) = D (b) A square with a side of length should be cut away from each corner to obtain the maximum volume. (Round to two decimal places as need inches inches inchesAcandy box is made from a piece of cardboard that measures 27 inches by 15 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? Complete parts (a) and (b). (a) The function to be minimized is A(s), where A is the surface area, and s is the side length of the square bottom. A(s) =(b) The dimensions of the tank with minimum surface area are E El (Simplify your answer. Use a comma to separate answers as needs A rectangular tank with a square base, an open top, and a volume of 19652 ft3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. (a) Find the formula of the function to be minimized (b) Find the dimensions of the tank that has the minimum surface area. A local club is arranging a charter ight to Hawaii. The cost of the trip is $620 each for 70 passengers, with a refund of $5 per passenger for each passenger in excess of 70. (3) Find the formula of the function to be maximized. (b) Find the number of passengers that will maximize the revenue received from the flight. (c) Find the maximum revenue. (a) The function to be maximized is R = , for p 2 70. (Type an expression using p as the variable.)