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 you get z 22 2 instead, then change your 2 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. For a certain company, the cost for producing z items is 40x + 300 and the revenue for selling a items is 80 -0.5x2. 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 a items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.
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 you get z 22 2 instead, then change your 2 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. For a certain company, the cost for producing z items is 40x + 300 and the revenue for selling a items is 80 -0.5x2. 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 a items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:To address the problem below, begin by copying the description of your company into Brightspace as your initial post. Follow up with your solution to all three parts (a, b, and c) of the problem. To copy the company description, use the "copy" function from this platform and then "paste" it into Brightspace. If you notice that \( x^2 \) is copied as \( x2 \), manually change it to \( x^2 \).
**Hint:** This topic relates to "2-1 Reading and Participation Activities: Quadratic Equations" in Module Two. Verify your answer to part b to ensure accuracy.
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**Problem Description:**
For a specific company, the production cost for \( x \) items is \( 40x + 300 \) and the revenue from selling \( x \) items is \( 80x - 0.5x^2 \).
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The company's profit is determined by subtracting the total costs from the total revenue. In economic models, a company is generally assumed to strive for profit maximization, or at the very least, to avoid loss.
**Part a:** Develop an expression to represent the profit from producing and selling \( x \) items, assuming that the company sells all produced items. (Hint: Expect a quadratic polynomial.)
Note: Ensure you evaluate each aspect to thoroughly understand how profit changes in response to varying quantities of produced and sold items.
![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).
\[ x = \]
**Part c:** Is it possible for the company to make a profit of $2,500?
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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).
\[ x = \]
**Part c:** Is it possible for the company to make a profit of $2,500?
Buttons:
- How Did I Do?
- Try Another
- Save
- Quit & Save
- Previous Unit Item
- Next Unit Item
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