Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3737 ft by 2020 ft. the resulting piece of cardboard is then folded into a box without a lid. find the volume of the largest box that can be formed in this way. b. suppose that in part (a) the original piece of cardboard is a square with sides of length s. find the volume of the largest box that can be formed in this way. a. to find the objective function, express the volume v of the box in terms of x.

a) The volume of the largest box that can be formed is .

b) The maximum volume of the box:

Explanation:

a) Length of the card board = l = 37 ft

Width of the card board= b = 20ft

Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.

Now, length of the box = L = 37 -2x

Breadth of the box ,B= 20- 2x

Height of the box ,H= x

Volume of the box ,V= L × B × H

Putting ,

x = 4.1537 , 14.846

When , x = 4.1537 , (maxima)

The volume of the largest box that can be formed:

The volume of the largest box that can be formed is .

b) Original piece of cardboard is a square with sides of length s.

Length of the card board = l = s

Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.

Now, length of the box = L = s -2x

Height of the box ,H = x

Volume of the box ,V= L × L × H

When , (maxima)

The maximum volume of the box: