Quadratic Question Dealing With Perimeter

  • Thread starter kylepetten
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  • #1
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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!
 

Answers and Replies

  • #2
tiny-tim
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hi kylepetten! :smile:
… 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! :wink:
 
  • #3
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hi kylepetten! :smile:


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

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

That what you meant?
 
  • #4
tiny-tim
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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 :wink:)

Yup! :biggrin:

So if 2x + y is constant, how do you maximise x2 + 2xy ? :wink:
 
  • #5
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(try using the X2 icon just above the Reply box :wink:)

Yup! :biggrin:

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

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.
 
  • #6
tiny-tim
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Yep, that should do it! :smile:
 
  • #7
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