Posted by **Brian** on Wednesday, April 4, 2012 at 11:45pm.

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 96 in. Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent via priority mail. Hint: The length plus the girth is 4x + h (see the figure below).

- Math -
**Steve**, Thursday, April 5, 2012 at 11:15am
well, we know

4x+h = 96, so h=96-4x

v = hx^2

= x^2(96-4x)

= 96x^2 - 4x^3

= 4(24x^2 - x^3)

dv/dx = 4(48x - 3x^2)

= 12x(16 - x)

dv/dx = 0 when x = 0 or 16

so, h = 96-4*16 = 32

So, if the package is 16x16x32

v = 8192 in^3

Now, technically, 4x+h <= 96, but it should be clear that max volume occurs when 4x+h is as large as possible.

## Answer This Question

## Related Questions

- Math - Postal regulations specify that a parcel sent by priority mail may have a...
- CALCULUS - Postal regulations specify that a package sent by priority mail may ...
- Math - Postal regulations specify that a package sent by priority mail may have ...
- Math Calculus - Postal regulations specify that a package sent by certain ...
- CALCULUS - 1. A rectangular package to be sent by a postal service can have a ...
- Trig - The postal service places a limit of 84 inches on the combined lenght and...
- Pre-Calc - A rectangular package to be sent by a delivery service can have a ...
- Algebra 2 - A package with square ends has combined length and girth(girth is ...
- algebra2 - A package with square ends has combined length and girth(girth is ...
- Calculus - Optimization - UBC parcel post regulations states that packages must ...

More Related Questions