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Questions and Answers
What is the primary role of the CFO in the context of this assignment?
What is the primary role of the CFO in the context of this assignment?
- To manage the sales team.
- To evaluate the financial implications of launching the new product. (correct)
- To design the product's marketing strategy.
- To oversee the production process.
Which function represents the total revenues collected from sales?
Which function represents the total revenues collected from sales?
- C(t)
- N(t)
- R(t) (correct)
- P(t)
Which of the following points would be significant for both the revenue and cost functions?
Which of the following points would be significant for both the revenue and cost functions?
- Local maxima
- Local minima
- Intercepts
- All of the above (correct)
In evaluating the profit function P(t), what is indicated by a local maximum?
In evaluating the profit function P(t), what is indicated by a local maximum?
What is a potential modification that could be applied to these models to improve them contextually?
What is a potential modification that could be applied to these models to improve them contextually?
What does the intercept of the cost function C(t) typically represent?
What does the intercept of the cost function C(t) typically represent?
What is the significance of local minima in the profit function P(t)?
What is the significance of local minima in the profit function P(t)?
Why is it important to graph the average profit function?
Why is it important to graph the average profit function?
Flashcards
Revenue Function
Revenue Function
The amount of money a company earns from the sale of a product or service over a period of time.
Cost Function
Cost Function
The amount of money a company spends on producing a product or service over a period of time.
Profit Function
Profit Function
The difference between revenue and cost. It represents the amount of money a company earns after covering its production costs.
Local Maxima/Minima
Local Maxima/Minima
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Y-intercept
Y-intercept
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End Behavior
End Behavior
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Average Profit Function
Average Profit Function
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Asymptote
Asymptote
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Study Notes
Polynomials Performance Task
- Main Task: Analyze revenue, cost, and profit functions for a new product launch.
- Revenue Function (R(t)): Models product revenue over time (in dollars)
- R(t) = -0.000004395t⁴ + 0.025466t³ – 45.157t² + 26121t
- Cost Function (C(t)): Models production costs over time (in dollars)
- C(t) = 0.000000899t⁴ – 0.006101t³ + 13.584t² – 10455t + 3400000
- Profit Function (P(t)): Calculated as R(t) - C(t)
- Determine profitability based on revenue and costs
- Analysis: Investigate intercepts, local maxima, minima, and end behavior of all functions within a business context.
- Technology: Use technology to graph and label functions.
- Significance: Interpret intercepts, extrema, and asymptotes for each function relating to the real-world scenario.
- Product Launch Decision: Use the analysis in the report to determine if the product launch is financially viable.
Extension Task
- Number of Units Function (N(t)): Models the number of units produced over time.
- N(t) = -0.000000034321t⁴ + 0.00021153t³ – 0.39687t² + 232.73t + 1000
- Average Profit Function (A(t)): Calculated as total profit divided by total units (P(t)/N(t))
- Analysis (Extension): Evaluate intercepts, local maxima, minima, and asymptotes of the number of units and average profit functions.
- Contextual Improvements: Suggest modifications to the models to make them more realistic.
- Product Launch Decision (Extension): Consider additional factors (number of units, average profit) to finalize launch decision.
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Description
In this performance task, you will analyze revenue, cost, and profit functions for a new product launch. Using polynomial functions, you'll investigate aspects such as profitability, intercepts, and extrema while utilizing technology for graphs. The results will help determine the financial viability of the product launch.
