Suppose an airline policy states that all baggage must be box shaped with a sum of length, width, and height not exceeding 174 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions? Write a function for the volume V of the box in terms of w, one of the edges of the square bottom. v= (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The length of the square-end edge is ☐ in. The box height is in. The greatest volume of the box is in.3. ? Enter your answer in each of the answer boxes.