My attempt: Volume of rectangular shape object = L * W * H Since we need to cut off length of x from four corners, therefore, the length is: 10 - x - x = 10 - 2x Since we need to cut off length of x from four corners, therefore, the width is: 8 - x - x = 8 - 2x The height is = x 1) So, the volume for the box in terms of x is: V = (10 - 2x) * x * (8 - 2x) = (10x - 2x^2) * (8 - 2x) = 80x - 20x^2 - 16x^2 + 4x^3 = 80x - 36x^2 + 4x^3 = 4x (20 - 9x + x^2) 2) The volume cannot be negative or 0: After substituting several values for x, the sensible values for x are x = 3, x = 2, x = 1 for volume to be non negative and non zero. 3) It does not make sense if x = 5. When x = 5, the volume will be = 0, the width of the box will be negative and the length will be 0. 4) As mentioned in 2), x = 1 is the smallest whole number value for non negative / non zero volume. The largest whole number value for x would be x = 3 since it is not sensible for x = 6 or x = 7 as the length (10 - 2x) and the width (8 - 2x) will be negative. 5) Therefore, if x = 2, the volume will be 48 cubic inch. That is the maximum sensible whole number volume. Since height = x, the height is = 2 inch.