You own a factory that is making a length of wire out of two metals: copper and iron. You have access to mines containing both iron and copper. The amount A you are able to produce is determined by the equation

A = 10000(sqrt(xy))

where x is the number of tonnes of copper mined and y is the number of tonnes of iron mined. However, you only have a limited number of mining resources. The amount of copper and iron you can mine is determined by the following relationship

x^2 + 4xy + 15y^2 = 144

If we mine more copper then we are forced to mine less iron. In this way we can think of y as a function of x. The quantity dA=dx represents the change in the amount of wire we can produce as we change the amount of copper.

(a) Find dA=dx as a function of x and y.
(b) Find the value of dA=dx when the amount of copper mined is equal to the amount of iron mined. Is it positive or negative? Should you mine more or less copper than this amount?

The bolded is, uhh, odd. Do you mean dA/dx?

anyway, for dA/dx just take the derivative of the first question with respect to x

then set x = y in the second equation (replace all y's with x's) and solve second equation for x

then plug that back into your dA/dx equation and solve for dA/dx

Yes, dA/dx is correct

dA/dx= 5000y(xy)^(-1/2)

This post was edited by JDota72 on Mar 27 2014 04:42pm