Awaste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 19y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

1.92 yd  x 3.83 yd  x 2.58 yd

Step-by-step explanation:

We have given a rectangular base, that its twice as long as it is wide.

It must hold 19 yd³ of debris.

Lets minimize the surface area, subject to the restriction of volume (19 yd³)

The surface is given by:

The volume restriction is:

replacing h in the surface equation, we have:

Derivate the above equation and set it to zero

The height will be:

Therefore,The dimensions that minimize the surface are:

Wide: 1.92 yd  

Long: 3.83 yd

Height: 2.58 yd