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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?

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.