We want to minimize the sum of two numbers given that we know its product, we will find that the minimum of the sum is 90
Finding the equations:
First, we need to define the variables we will be using, let's define A as the first number and B as the second number.
Then we can write the product as:
A*B = 675
And we want to minimize:
A + 3*B
Minimizing the sum:
To do it, we first need to isolate one of the two numbers in the product, let's isolate A:
A = 675/B
Now we can replace this on the sum to get:
675/B + 3*B
To minimize this we just need to find the zeros of the first derivate, the first derivate is:
-675/B^2 + 3
And we need to make this equal to zero:
-675/B^2 + 3 = 0
675/B^2 = 3
675/3 = B^2
225 = B^2
√225 = B = 15
So the value of B that minimizes the sum is B = 15, and the minimum sum is:
675/15 + 3*15 = 90
If you want to learn more about minimizing, you can read:
https://brainly.com/question/25207394
