Thread: 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.

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.

Write one value in terms of the other.



Then substitute to obtain an equation in one variable.



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.