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Section2.4Decision Report 2

¶In your previous decision report (Section 1.2), your team constructed a table of data relating quantities \(q\) (in thousands) and prices \(p\) (in dollars per unit) for your product's projected sales on the national market.

Now, your team's job is to *extrapolate* from that data: to determine a mathematical function

\begin{equation*}
p = D(q)
\end{equation*}
which best fits your table of data. This function is known as a **demand function**, and its job is to capture the relationship between the unit price charged for a product, and the quantity of product that would sell at that price.

Your Vice President of National Sales remains somewhat unconvinced by your previous findings, in which you determined whether a national sales goal of 1.5 million units was realistic. Your job in this decision report is to make an even stronger case for your previous results.

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1Decision Report 2: What are the worst-case scenarios?

*Download:* Click to download this Decision Report assignment (PDF).

*Decide:* Reinforce your decision from Exercise 1.2.1.1 by determining both

- The maximum price that is possible to charge for your product in the national market, and
- The maximum quantity that is possible to sell in the national market.

Explain your findings, and why they support your previous decision report, in a brief memo to your Vice President.

*Deliver:* Use a trend line in either *Excel* or *Desmos* to fit a quadratic function to your national market data, with quantity \(q\) (in thousands) on the horizontal axis and price \(p = D(q)\) on the vertical.

Report both the equation of this quadratic, using the variables \(q\) and \(p\) in place of \(x\) and \(y\text{,}\) its correlation coefficient, and the computations that inform your decision.