calc

Applied Optimization An open-top box is to be made from a 26 in. by 22 in. rectangular peice of cardboard by removing a square with side length x from each corner and folding up the remianing flaps on each side. What size square should be cut out from each corner to get a box with maximum volume and after removing that square, what will the maximum volume be? Start by writing the volume of the box in terms of . After removing the squares of side length a from each corner and folding up the flaps, the volume of the box, as a function of x is: V(x) = in2 The length of the side of the squares that were cut out to obtain the maximum volume would be: I = in After removing the squares of side length x indicated above and folding up the remaining flaps, the volume of the box is: V =in NOTE: you may enter an exact value for the answer in this problem or you may use decimals. If you use decimals, makes ure to use a large number of decimals in your answer, say 4 or 5 to be on the safe side