Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then V = xyz . . . (1) 2z + x = 16 => x = 16 - 2z . . . (2) 2z + y = 30 => y = 30 - 2z . . . (3)
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard. The maximum volume is 725 25/27 (725.9) cubic inches.