An engineer must design a rectangular box that has a volume of 9 m3 and that has a bottom whose length is twice its width. What are the dimensions of the box so that the total surface area (of all six sides) of the box is minimized

    and  

Explanation:

Given

Represent the height as h, the length as l and the width as w.

From the question:

Volume of a box is calculated as:

This gives:

Substitute 9 for V

Make h the subject:

The surface area is calculated as:

Recall that:

Recall that:

So:

To minimize the surface area, we have to differentiate with respect to w

Set A' to 0

Add to both sides

Multiply both sides by

Make the subject

Solve for w

Recall that :   and

Hence, the dimension that minimizes the surface area is:

    and  

do you have any options?

answer:

the army does care about its soilders sir i think yout getting off on the wrong foot sir you need to respect our country were keeping the peole that want to d harm towards you out. so dont go saying we don't care cause we do