Finding the least possible sum of a product.

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Homework Help Overview

The problem involves finding two positive numbers whose product is 100, with the goal of minimizing their sum. The context is rooted in calculus, specifically in optimization problems.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to clarify the problem statement and expresses confusion about the wording. They outline their understanding of the task and seek feedback on their reasoning.

Discussion Status

Participants are providing feedback on the clarity of the original poster's work. There is acknowledgment of the correctness of the approach, despite some confusion in the presentation. The discussion is ongoing, with participants engaging in clarifying the original poster's thought process.

Contextual Notes

There is mention of the original poster's struggle with organizing their work, which may affect the clarity of their mathematical reasoning. The thread has been moved to a more appropriate section for calculus discussions.

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Homework Statement


The product of two positive numbers is 100. What numbers will produce the least possible sum? Confirm that the sum is in fact a minimum.

Homework Equations

The Attempt at a Solution


For this question here I feel like the wording is a bit confusing, I tried my best please let me know if I'm on the right track and if there is any mistakes we can work through.
Anyways here's my train of thought:
From my understanding it is asking me to find two positive numbers that have a product of 100. Basically two numbers when multiplied together equal 100, and the two numbers need to have the lowest possible sum when added together.
Here's my work:
1qeYxiY.png
 

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What you posted is a bit hard to follow (it doesn't appear to be first column followed by second column, but rather some back and forth), but overall it appears correct.
 
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DrClaude said:
What you posted is a bit hard to follow (it doesn't appear to be first column followed by second column, but rather some back and forth), but overall it appears correct.
That is true, I'll be sure to put the math in order from now on. I wrote that when I first woke up. I wasn't thinking straight, it looks like I'm still doing math in my dreams, which is also extremely unorganized/confusing but correct.
I appreciate your help kind sir.
 
Thread moved to Calc & Beyond section.
 

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