Question

"You are making boxes and begin with a rectangular piece of cardboard that measures 1.75 meters by 1.25 meters. From each corner of that rectangular piece you cut out a square piece that is 0.25 meter on a side, as shown. You fold up the "flaps" to form a box without a lid.

What is your estimate of the size of the square corner cuts that will give a box with the
largest volume?"

Image + work attached in comments

Answer 1

volume = lwh
So the equation I have set up is,
(1.75 + -2x)(1.25 + -2x)(x) = Volume

I'm not sure where to go from here.

Answer 2

I guess, multiply that out, take the first derivative, set it to 0, find the x value of the maximum.

Answer 3

Thank you - does this look like the correct form multiplied out?
(2.1875x -6x2 + 4x3) = V

Answer 4

yes

Answer 5

Thank you

Answer 6

yw

Answer 7

This is my derivative of the equation - 12x^2 - 12x + 2.1875 ,
I'm not sure how to set it to zero or find the max. Do I literally just set the equation equal to zero?

Answer 8

yes. And then use the quadratic formula

Answer 9

Ohh okay. So now I have x = \[-12 \pm \sqrt{(-12)^{2}-4(12)(2.1875)}\div 2(12)\]

Answer 10

with X = approx. 0.7602 and 0.2398 for final answers

Answer 11

So each of these would maximize the volume of the box as measurements of cut corners?

Answer 12

Yes. I agree with that.

Answer 13

Ah perfect! Thank you so much for the help!

Answer 14

Now just a minute. Which one is the answer?

Answer 15

It must be .2398, because .7602 would be too large - subtracting it twice from the width would result in a negative width

Answer 16

You are correct. Very good.

Answer 17

Thank you again!

Answer 18

yw