# Problem with creating a formula

• Jan 15th 2011, 06:31 AM
Mathmen
Problem with creating a formula
Question:

Attachment 20448

a) We have a folded box shaped like a rectangle with the length b and width a. The box has four squares that we fold up, these squares are the height of the box x. Choose a couple of values for length b and width a and decide what x has to be in order for the box to have the largest volume.

b) Produce a formula that enables you to calculate what x has to be in order to get the largest volume when only given the length a and width b.

My attempt to a solution:

a)

1. First i got to make a function that describes the volume of the box
2. Derive the function in order to find the maximum point of the function
3. Find out which x-values that can't be a part of the solution (this is where my first problem lies) for example that x > 0 but can't be larger than...
4. If both x values are a part of the solution, then find out which one lies at a maximum point and finding the y coordinate by inserting the x value into the normal function.

Length: b-2x
Width: a-2x
Height: x

Attempt 1:

y= x(b-2x*a-2x)
y= x(ab + b*-2x + a*-2x +4x^2)

I then chose a = 20 b = 5 (measured in cm) this gave me

y= x(20*5 +5*-2x -20*-2x +4x^2)
y= 4x^3 -50x^2 +100x
y´= 12x^2 -100x +100
y´= x^2 - 25/3x + 25/3

When solving the equation using the quadratic formula i get x= 1,16 and x= 7,16 and when searching for the maximum point i get that when x= 1,16 we're at a maximum point which gives us y = 54,94. The maximum volume being 54,94cm^3 when x = 1,16.

Attempt 2:

a= 10
b=5

On attempt 2 i got x = 3,94 and x= 1,05 and the maximum point was at x= 1,05 and y= 54,5

Attempt 3:

a= 40
b= 20

On attempt 3 i got x= 15,77 x= 4,22 and the maximum point was at x= 4,22 and y= 1539,59.

b) This is where my problem lies, creating a formula where i only need a and b to get what x needs to be in order to get the maximum volume

• Jan 15th 2011, 06:35 AM
Mathmen
I apologize I just noticed that my attachment didn't go through. It was more or less just a picture of a folded box shaped as a rectangle with the length b and width a. At each corner there were small squares with the length x
• Jan 15th 2011, 06:37 AM
Prove It
Are you allowed to use Calculus?
• Jan 15th 2011, 06:39 AM
Mathmen
I'm allowed to use any method as long as it works with the examples above
• Jan 15th 2011, 10:33 AM
Mathmen
I solved thanks anyways
• Jan 15th 2011, 10:33 AM
wonderboy1953
The underlying question
Quote:

Originally Posted by Mathmen
I'm allowed to use any method as long as it works with the examples above

I think the underlying question is whether you studied calculus yet?