Exhibit 7-3
a Company Has the Following Historical Data on the Number

question 27

Essay

Exhibit 7-3
A company has the following historical data on the number of ad exposures and the corresponding number of units sold of one of its products:
$$\begin{array}{l}\text { Historical }\\\begin{array} { | c | c | } \hline \text { Ads } & \text { Units } \\\hline 0 & 3 \\\hline 20 & 18 \\\hline 40 & 34 \\\hline 60 & 46 \\\hline 80 & 56 \\\hline 100 & 65 \\\hline 120 & 72 \\\hline 140 & 78 \\\hline 160 & 82 \\\hline 180 & 85 \\\hline 200 & 90 \\\hline 220 & 90 \\\hline 240 & 93 \\\hline 260 & 94 \\\hline 280 & 95 \\\hline 300 & 101 \\\hline 320 & 98 \\\hline 340 & 100 \\\hline 360 & 98 \\\hline 380 & 101 \\\hline 400 & 105 \\\hline\end{array}\end{array}$$
-[Part 2] Refer to Exhibit 7-3.Formulate a nonlinear optimization model to find the parameters of a function of the form: f(x)= a(1 − e−bx)to model demand for its product as a function of ad exposures (x).In terms of fit,is this model better or worse than the model in Part 1
Explain your answer

---

Definitions:

Opportunity Costs

The cost of choosing one option instead of the next best alternative, representing the benefits missed out on.

Certainty Equivalent Factors

The adjusted value of risky outcomes to reflect the investor's risk aversion, often used in capital budgeting.

Life Span

The duration or length of life of an organism, object, or system, often used in the context of product life cycles or human longevity.

Portfolio

In finance, a collection of investments.