The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

*Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.

Question

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

*Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.

haleyelizabeth2017 · Answer

@TQKMB this is the question...

haleyelizabeth2017 · Answer

@SolomonZelman :/ so for the first equation wouldn't it be x+1.5x+y=6 or 2.5x+y=6?

solomonzelman · Answer

"If the length must be 1.5 times the height"  $\large\color{black}{  l=1.5w    }$
"the sum of the dimensions at 6 inches"   $\large\color{black}{  l+w +h=6   }$

solomonzelman · Answer

$\large\color{black}{  1.5w+w +h=6   }$
$\large\color{black}{  2.5w+h=6   }$

solomonzelman · Answer

and you want to find a maximum value with (will say of a surface) when your dimensions are 2.5 and 6.

looks like an optimization problem?

solomonzelman · Answer

I mean not dimensions 2.5 and 6, but w and h

solomonzelman · Answer

Is this calculus?

haleyelizabeth2017 · Answer

oops! So sorry....no it is not....it's Honors Algebra 2

solomonzelman · Answer

well, either way, you want to find all dimensions in terms of 1 variable, and you have a 3D box, that right? or 2D box?

haleyelizabeth2017 · Answer

this section is polynomials and polynomial functions...

haleyelizabeth2017 · Answer

ummm.....I'm not sure....what I put in the question is all they gave me :(

solomonzelman · Answer

if it is algebra 2, then there are only 2 dimensions, because they don't want to do optimization problem from calc 1, although it is a very typical optimization prob from calc.

$\large\color{black}{  l=1.5w   }$
$\large\color{black}{  l+w=6   }$
$\large\color{black}{  1.5w+w=6   }$
$\large\color{black}{  2.5w=6   }$
$\large\color{black}{ w=2.4   }$

$\large\color{black}{ l=2.4\times 1.5=3.6   }$

solomonzelman · Answer

well, I don't understand then, why do are you given that you want the maximum volume if you already have 2 equations given (1. sum of Dimensions is 6,  2. length is 1.5 times greater than the width)  ?

solomonzelman · Answer

see what I am asking ?

haleyelizabeth2017 · Answer

I'm not sure :( this is just super confuzzling

solomonzelman · Answer

But on the other hand, it can't be an optimization problem with 3 dimensions, because you are just in alg 2.

solomonzelman · Answer

I would say just 2 dimensions, the way I did it.

haleyelizabeth2017 · Answer

okay...

haleyelizabeth2017 · Answer

Is that all I have to do?

solomonzelman · Answer

apparently.

haleyelizabeth2017 · Answer

okay thank you so much!

solomonzelman · Answer

yw