You should come up with the following substitution for length of side of square such that:

l=x

h represents the height of the package

The problem provides the following information about postal requirements such that:

275 = h + 2(h + xsqrt2)

Notice that 2(h + xsqrt2) represents the cross sectional perimeter...

## See

This Answer NowStart your **subscription** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

You should come up with the following substitution for length of side of square such that:

l=x

h represents the height of the package

The problem provides the following information about postal requirements such that:

275 = h + 2(h + xsqrt2)

Notice that 2(h + xsqrt2) represents the cross sectional perimeter of the package.

Opening the brackets yields:

275 = 3h + 2sqrt2*x

You need to evaluate the volume of rectangular package such that:

V = x^2*h

You should use the equation that expresses the postal requirement to write h in terms of x such that:

`3h = 275 - 2sqrt2*x => h = (275 - 2sqrt2*x)/3`

You need to substitute `(275 - 2sqrt2*x)/3 ` for h in equation of volume such that:

`V = x^2*(275 - 2sqrt2*x)/3`

You need to optimize the volume, hence, you need to differentiate the function of volume with respect to x such that:

`V'(x) = 2x*(275 - 2sqrt2*x)/3- 2sqrt2*x^2/3`

`V'(x) = 550x/3 - 4sqrt2*x^2/3 - 2sqrt2*x^2/3`

`V'(x) = 550x/3 - 6sqrt2*x^2/3`

You need to solve for x the equation `V'(x) = 0` such that:

`V'(x) = 0 => 550x/3 - 6sqrt2*x^2/3 = 0`

`550x - 6sqrt2*x^2 = 0`

You need to factor out `2x` such that:

`2x(275 - 3sqrt2*x) = 0 => x = 0 ` invalid

`275 - 3sqrt2*x = 0 => x = 275/(3sqrt2) => x = 275sqrt2/6` inches

**Hence, evaluating the dimension that meets the postal requirements yields `x = 275sqrt2/6` inches.**