# Math Help - Optimization problem

1. ## Optimization problem

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.

2. Originally Posted by av8or91
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.

$xy=110$

$x+2y=minimum$

Write one value in terms of the other.

$y=\frac{110}{x}$

Then substitute to obtain an equation in one variable.

$x+2\frac{110}{x}=x+\frac{220}{x}=x+220x^{-1}$

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.