Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 15 inches by b = 11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of a that results in a box the maximum volume. Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume V as a function of a: V = (15 - 2x) (11 - 2x)x (2) Determine the domain of the function V of a (in interval form): (3) Expand the function V for easier differentiation: V = 4x3 - 52x + 165x (4) Find the derivative of the function V: V'= 12x - 104x + 165 (5) Find the critical point(s) in the domain of V: (6) The value of V at the left endpoint is (7) The value of V at the right endpoint is (8) The maximum volume is V = (9) Answer the original question. The value of a that maximizes the volume is