A. squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 27 ft by 15 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:

b) The maximum volume of the box:

Explanation:

a) Length of the card board = l = 27 ft

Width of the card board= b = 15 ft

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 = 27 -2x

Breadth of the box ,B= 15 - 2x

Height of the box ,H= x

Volume of the box ,V= L × B × H

Putting ,

x = 10.9051, 3.0949

When , x = 3.095 , (maxima)

The volume of the largest box that can be formed:

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:

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

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