Weekly Math Problem #74

Profit. As I browse my many materials, I landed upon a word problem. This one has a financial application to it. Nothing to be too concerned about...even if you don't have a financial background, you will be able to understand it. Your algebra background is far more important, in this case. 

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to solve a quadratic equation        

             

WMP! #74 says...

Happy solving!

Check back on Saturday, February 19th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Alright folks, let's get into this solution... 

Step 1:  Find the profit function

Step 2:  Setup the specified profit condition

This quadratic equation can be solved using two methods.

Step 3a:  Solve via the factoring

Step 3b:  Solve via quadratic formula

Step 4:  Answer the question

With the given conditions of revenue and cost for the company, it is found that a profit of $300 will be generated by producing either 20 or 60 units of product.

Here is plot of the profit function:

** This plot was generated using Geogebra.org's calculator. **

▪️ Were you able to find the two values of x?
▪️ If so, what method did you use?

▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
WMP! #75 is up next. 🏌🏿‍♀️

Cheers!

The Younge Lady

Weekly Math Problem! #6

Quadratic Function Application. One of the things that people cannot stand in mathematics, next to fractions is...dare I say it...⚠️word problems⚠️. 🙄 Trust me I get it! 😒 I've encountered hundreds, if not a few thousand, words problems over the years I've been doing mathematics. I'm talking about word problems from algebra, geometry, precalc, calc, differential equations, linear algebra, statistics, standardized tests such as the SAT and GRE, not to mention word problems from the sciences. And still, when I see a word problem, my insides jump just a little bit. It can definitely be tricky to relate the words you're seeing in a problem to some math formula/techniques that you'll need to solve the word problem. If you're super annoyed with word problems, leave a comment down below 👇🏿 and vent a bit.

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  How to convert words/phrases to algebraic expressions

    ✔️  How to solve a quadratic equation

    ✔️  How to find the minimum/maximum value of a quadratic function

You will also need to know a little finance vocabulary, which can be easily looked up. Here goes WMP! #6... 

Happy solving! 

Check back on Friday, June 12th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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One of the things that will be helpful when solving a problem is identifying and marking the words/phrases that can be translated into algebraic expressions/equations. In the solution, the key phrases are denoted in blue. 

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Below is the graph of R(x): 

*This graph was generated on Desmos.com.*

The graph of the function isn't part of the original question, however it's great if you can have a visual to confirm or deny the answers you came up with. I showed the point on the graph where no revenue is generated, which is one of the roots (or "zeros") of the function. I also showed the point on the graph where maximum revenue is generated, which is the maximum point (or turning point).

◾️ How did you find this word problem?? Easy? Hard? In between? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

See you again, soon, for WMP! #7 🤓

Cheers!

The Younge Lady