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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.

### Subsection2.4.1Exercises

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

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.