(Solved): Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a recta ...

Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a rectangular box, they measure the girth plus the length and multiply the result by \( \$ 0.55 \). For a box with a square crosssection (measuring \( x \) inches to a side) and costing \( \$ 220 \) to ship, the function \( V(x)=x^{2}(400-4 x) \) gives the volume of the box (in cubic inches). Find the values of \( x \) that are physically possible for such a box (called the relevant domain). Enter your answer as an interval with open parentheses: Use the first derivative to determine where the function \( V(x) \) is decreasing (within the relevant domain). Enter your answer as an interval with open parentheses: Use the second derivative to determine where the function \( V(x) \) is concave up (within the relevant domain). Enter your answer as an interval with open parentheses: Find the maximum volume we can ship for \( \$ 220 \) (having square cross-section). cubic inches