Polynomials Performance Task: Revenue & Cost Analysis

What is the primary role of the CFO in the context of this assignment?

Which function represents the total revenues collected from sales?

Which of the following points would be significant for both the revenue and cost functions?

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 does the intercept of the cost function C(t) typically represent?

What is the significance of local minima in the profit function P(t)?

Why is it important to graph the average profit function?

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.

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.