Among all pairs of numbers with a sum of 149, find the pair whose product is max

boitshupoO

boitshupoO

Answered question

2021-09-23

Among all pairs of numbers with a sum of 149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Answer & Explanation

SchulzD

SchulzD

Skilled2021-09-24Added 83 answers

Step 1
given that sum of all pair of numbers is 149
and product of pair is maximum
find the pair and write interms of fractions
Step 2
let x and y be two numbers then
x+y=149
xy=max
from x+y=149
x=149y
substitute in product term
(149y)y=149yy2
(149y)y=(y2149y)
(149y)y=(y2149y+(492)2)+1492
(149y)y=(y1492)2+1492
the expression is maximum at 1492 when (y1492)2=0
y=1492
x=1491492
x=1492
maximum product is x=y=1492

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?