Find two positive numbers satisfying the given requirements. the product is 1200 and the sum of the first plus three times the second is a minimum.

You want to minimize the function for subject to the constraint .

By solving the constraint you get . So you need to minimize the one-variable function .

Compute the derivative . The derivative is zero when . You need so you get only one critical point .

Since you get that for all and since you get that for all .

That means that has a minimum at . So the desired numbers are and .

Could you make it more clear?