Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:### Module Three Discussion Question
**Solve the problem below.**
For your initial post in Brightspace, copy the description of your company given in the box below and then enter your solution to all three parts (parts a, b, and c) of the problem. To copy the description of your company, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work. However, if when you copy and paste \( x^2 \) you get \( x2 \) instead, then change your \( x2 \) to \( x^2 \).
**Hint:** We covered this topic in "2-1 Reading and Participation Activities: Quadratic Equations" in Module Two. You can check your answer to part b to make sure that you are on the right track.
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For a certain company, the cost for producing \( x \) items is \( 45x + 300 \) and the revenue for selling \( x \) items is \( 85x - 0.5x^2 \).
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The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
**Part a:** Set up an expression for the profit from producing and selling \( x \) items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
![The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
**Part a:** Set up an expression for the profit from producing and selling \( x \) items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
**Part b:** Find two values of \( x \) that will create a profit of $50.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or \( x + 1; x - 1 \)). The order of the list does not matter. To enter \(\sqrt{a}\), type sqrt(a).
\( x = \) [Input field]
**Part c:** Is it possible for the company to make a profit of $2,500?](https://content.bartleby.com/qna-images/question/2f332ee6-3ef6-4e55-bad3-1cebde5ee541/e5341802-9456-47fd-ac0f-ba6b73d7aa4b/j01wsoa_processed.jpeg)
Transcribed Image Text:The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
**Part a:** Set up an expression for the profit from producing and selling \( x \) items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
**Part b:** Find two values of \( x \) that will create a profit of $50.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or \( x + 1; x - 1 \)). The order of the list does not matter. To enter \(\sqrt{a}\), type sqrt(a).
\( x = \) [Input field]
**Part c:** Is it possible for the company to make a profit of $2,500?
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