4th-class parsel:girth plus length <= 108; find largest vol

[methodical]

According to postal regulations, the girth plus the length of a parsel sent by fourth-class mail may not exceed 108 in. What is the largest possible volume of a rectangular parsel with two square sides that can be sent by fourth-class mail?

I am clueless. :?

 

[mmm4444bot]

I dont know where to start with this word problem ...

... I am clueless ...

Hello Methodical:

Do you understand the definition of the word "girth"? I'm wondering why you are not able to begin anything at all on this exercise.

If only two sides of the box are squares, then we can say that the box has dimensions L by W by W, for example.

Use this information to write an expression set equal to 108.

Solve that equation for the appropriate variable, and then write an equation using the formula for volume.

After you take the derivative, you will get a quadratic.

Cheers,

~ Mark



MY EDIT: Resolved misleading ambiguity

 

[methodical]

Thanks my results are...

V = x2y.

V (x) = x2(108 ? 4x) = 108x2 ? 4x3.

V ?(x) = 216x ? 12x2 = x(216 ? 12x).

The only critical points x = 0 or x = 18.
V (18) = 11664,

The maximal volume of the parcel is 11664 in2.

 

[mmm4444bot]

Good job.

Please use the caret symbol (^) to indicate exponentiation (shift-six on most keyboards).

EG:

x * x * y = x^2 * y