# Struggling with Math Homework

• December 1st 2008, 12:02 PM
rlder35
Struggling with Math Homework
I have two math problems that have me STUMPED! Can anyone help??

Find the elasticity of demand when p=5 if demands if modeled by q= (250/p^2)-6

A cylindrical can is to hold 4PIE cubic inches of frozen concentrate orange juice. The cost per square inch of constructing the metal top and bottom is twice the cost per square inch of constructing the cardboard side. What are the dimensions of the least expensive can?

ANY help is greatly appreciated!!
• December 1st 2008, 12:09 PM
Shyam
Quote:

Originally Posted by rlder35
I have two math problems that have me STUMPED! Can anyone help??

Find the elasticity of demand when p=5 if demands if modeled by q= (250/p^2)-6

$q = \frac{250}{5^2}-6$

$q=10-6$

$q=4$
• December 1st 2008, 12:18 PM
rlder35
This problem involved calculating derivatives, which is where I ran into trouble. To solve this, i have to solve (dQ/dP)*(p/q). Once I get an answer, than I plus the p=5 in. Calculating the initial equation has been very difficult for me.
• December 1st 2008, 12:19 PM
Shyam
Quote:

Originally Posted by rlder35
I have two math problems that have me STUMPED! Can anyone help??

A cylindrical can is to hold 4PIE cubic inches of frozen concentrate orange juice. The cost per square inch of constructing the metal top and bottom is twice the cost per square inch of constructing the cardboard side. What are the dimensions of the least expensive can?

ANY help is greatly appreciated!!

Volume, $V = 4\pi \;\;in^3$

$\pi r^2 h = 4\pi$

$h=\frac{4\pi}{\pi r^2}$

$h = \frac{4}{r^2}$ .....................(1)

Now, surface area , $A= 2\pi r^2+2\pi rh$

Cost $C= 2\pi r^2\times 2+2\pi rh$

$C = 4\pi r^2 +2\pi r \left(\frac{4}{r^2}\right)$

$C = 4\pi r^2+\frac{8\pi}{r}\;\;\;$ Now, minimize this cost.
• December 1st 2008, 12:21 PM
rlder35
That's exactly the point where I started to get stumped. Should I solve for a certain variable here?
• December 1st 2008, 12:28 PM
Shyam
Quote:

Originally Posted by rlder35
That's exactly the point where I started to get stumped. Should I solve for a certain variable here?

take different values of r to get different C. Make a table of values of r and C.

The minimum C will be when r = 1 inch

now, from eqn (1), h = 4/1^2 = 4 inch.
• December 1st 2008, 12:31 PM
buddyboy
diff c then set equal to zero and solve for r

does that help
• December 1st 2008, 02:10 PM
rlder35
Any more help??
Can anyone help out with the first problem, elasticity of demand? I can't get anywhere!!
• December 1st 2008, 03:08 PM
buddyboy
hope this is what you are looking for