The sum is 110.Find two positive real numbers whose product

Lincoln Hernandez

Lincoln Hernandez

Answered question

2022-02-01

The sum is 110.Find two positive real numbers whose product is a maximum.

Answer & Explanation

illustrationsamk

illustrationsamk

Beginner2022-02-02Added 14 answers

Let x and y be the requested numbers then
Sum =x+y=100y=100x
Their product is given by
Product (P(x))=x×y
P(x)=x(100x)
P(x)=100xx2
We see that P(x) is a quadratic of x, we know quadratics achieve
their extremum (Max or Min) when
x=b2a
In our case b=110 and a=1<0
So, we get maximum product for
x=1102(1)=55
y=110-x=55
x=55, y=55

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