Find 2 positive numbers whose product is 110 and the sum of the first plus twice the second is a minimum.
This problem is really confusing. Any help greatly appreciated.
$\displaystyle xy=110$
$\displaystyle x+2y=minimum$
Write one value in terms of the other.
$\displaystyle y=\frac{110}{x}$
Then substitute to obtain an equation in one variable.
$\displaystyle x+2\frac{110}{x}=x+\frac{220}{x}=x+220x^{-1}$
Now, differentiate this and find the x for which the derivative is zero.
This gives the value of x corresponding to the minimum value of x+2y=110.
Then use this x to find y.