Question 720885: find two positive numbers with a product of 185 and the sum is a minimum. round of your answer in 4 decimal places. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! I hope you know some Calculus because I can;t think of any other way to solve this. If you don't know Calculus then re-post the question and say that the solution cannot use Calculus.
If the two numbers are x and y, then the fact that their product is 185 would translate into:
x*y = 185
Solving for y this would give us:
y = 185/x
The equation for the sum of x and y would be:
s = x + y (where "s" is the sum)
Substituting the expression we found for y gives us:
To find a minimum sum we will find the first derivative...
...set it to zero...
... and solve for x: or
Since x (and y) must be positive numbers, we reject the negative solution. Using and solving for y gives us
There are various ways to check if this is a minimum and not a maximum. One way is to pick a different pair of positive numbers whose product is 185. For example, 1 and 185. The sum of these two is 186. Since the sum of two of them will be less than 28, far less than the sum of 1 and 185.
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