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Suppose a business can sell x gadgets for p = 250 - 0.01x dollars apiece, and it costs the business c(x) = 1000 + 25x dollars to produce the x gadgets. Determine the production level and cost per gadget required to maximize profit. O A. 13,750 gadgets at $112.50 each O B. 11,250 gadgets at $137.50 each O C. 111 gadgets at $248.89 each O D. 10,000 gadgets at $150.00 eachThe strength S of a rectangular wooden beam is proportional to its width times the square of its depth. Find the dimensions of the strongest beam that can be cut from a 10-in-diameter cylindrical log. (Round answers to the nearest tenth.) O A. w= 6.8 in; d =7.2 in O B. w= 5.8 in; d = 8.2 in O C. w= 4.8 in; d = 9.2 in 10 d O D. w= 6.8 in; d = 9.2 inOf all rectangles with a perimeter of 18, which one has the maximum area? (Give the dimensions.) The rectangle that has the maximum area has length and width (Simplify your answers.)Of all rectangles with a fixed perimeter of P, which one has the maximum area? (Give the dimensions in terms of P.) The rectangle that has the maximum area has length and widthFind positive numbers x and y satisfying the equation xy = 35 such that the sum 5x + y is as small as possible. The numbers are x = and y = (Type exact answers, using radicals as needed.)A rectangular tank with a square base, an open top, and a volume of 2,048 ft" is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function. A = (Type an expression.) The interval of interest of the objective function is. (Simplify your answer. Type your answer in interval notation.) The tank with the minimum surface area has a height of oft and a square base with a sidelength of |ft