Struggling with Math Homework

rlder35 · #1 $Old$ December 1st, 2008, 01:02 PM

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!!

Shyam · #2 $Old$ December 1st, 2008, 01:09 PM

Quote:

Originally Posted by rlder35 $View Post$

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

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

$q=10-6$

$q=4$

rlder35 · #3 $Old$ December 1st, 2008, 01:18 PM

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.

Shyam · #4 $Old$ December 1st, 2008, 01:19 PM

Quote:

Originally Posted by rlder35 $View Post$

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.

rlder35 · #5 $Old$ December 1st, 2008, 01:21 PM

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

Shyam · #6 $Old$ December 1st, 2008, 01:28 PM

Quote:

Originally Posted by rlder35 $View Post$

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.

buddyboy · #7 $Old$ December 1st, 2008, 01:31 PM

diff c then set equal to zero and solve for r

does that help

rlder35 · #8 $Old$ December 1st, 2008, 03:10 PM

Can anyone help out with the first problem, elasticity of demand? I can't get anywhere!!

buddyboy · #9 $Old$ December 1st, 2008, 04:08 PM

hope this is what you are looking for