Quadratic Question Dealing With Perimeter

[kylepetten]

Homework Statement

Jillian is getting ready to send a holiday package in the mail. The rectangular package has a square base and the sum of all the edges of the package measures 140 cm. What dimensions will produce a package with the largest possible surface area?

Homework Equations

Let x = widths and y = heights

The Attempt at a Solution

P=8x + 4y
140 cm = 8x +4y
-4y = 8x - 140 cm
y = -2 + 35 cm

This is as far as I can get. Am I supposed to solve for x? Please lend me a hint. Thanks a bunch!

 

[tiny-tim]

hi kylepetten!

… What dimensions will produce a package with the largest possible surface area?
…
P=8x + 4y
140 cm = 8x +4y
-4y = 8x - 140 cm
y = -2 + 35 cm

This is as far as I can get.

ok so far … and now you need an expression for the area!

 

[kylepetten]

hi kylepetten!


ok so far … and now you need an expression for the area!

SA = x^2 + x^2 + xy + xy + xy + xy
SA = 2x^2 + 4xy

That what you meant?

 

[tiny-tim]

SA = x^2 + x^2 + xy + xy + xy + xy
SA = 2x^2 + 4xy

That what you meant?

(try using the X² icon just above the Reply box )

Yup!

So if 2x + y is constant, how do you maximise x² + 2xy ?

 

[kylepetten]

(try using the X² icon just above the Reply box )

Yup!

So if 2x + y is constant, how do you maximise x² + 2xy ?

Am I off track by saying fill in -2x+35 for y?

Then use x = -b / 2a ?

Thanks for all the help, by the way.

 

[tiny-tim]

Yep, that should do it!

 

[kylepetten]

Yep, that should do it!

Thanks a lot!