Quadratic word problem

[Cubby208]

Hello I have a word problem on my homework I am stuck on

A sand company has decided to store their sand in boxes. However because of unknown reasons the width of the box must be 1.5 times the length of the box. Furthermore the sum all all three sides must be less than 6.75. What dimensions would best maximize the volume of these boxes?

please show as much work and thought process as possible.

 

[Cubby208]

showing work and thought process is your job not ours.

3 parameters to play with, length L, width W, height H.

volume = L * W * H

W = 1.5 * L

it should be pretty clear to maximize the volume we want the sum of all the sides to be as large as possible so we set that sum to be the maximum of 6.75 allowed.

L + W + H = 6.75

Given these 2 constraint equations you can get the volume all in terms of 1 variable.

What have you learned in class about maximizing functions?

@Romesk;349640
i got the same system of equations...
however how do I get that into a quadratic? I don't see anything to foil.

 

[JeffM]

@Romesk;349640
i got the same system of equations...
however how do I get that into a quadratic? I don't see anything to foil.

Romesk suggested that you express the volume in terms of one variable. Did you do that? What did you get?