The sum of the first and three times the second is 42 2 positive numbers whose product is a maximum

Nyasia Flowers

Nyasia Flowers

Answered question

2022-09-03

The sum of the first and three times the second is 42
2 positive numbers whose product is a maximum

Answer & Explanation

Raven Mosley

Raven Mosley

Beginner2022-09-04Added 14 answers

Call x the first number, y the second.
For first statement, we get:
x+3y=42
For second statement:
xy is a maximum.
From first equation, solve for x:
x=42-3y
Plug into second.
( 42 3 y ) ( y ) = 42 y 3 y 2
This is a parabola. The maximum value occurs at -b/2a which is -(42)/2(-3) = 7.
y=7.
x=42-3(7)=21
So x=21. y=7.

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