$1.$ ?Quarterly sales of Kohl $$ s $,$ ?in millions of dollars, are shown below. $(6$ ?points $)$

?Quarter $1$ ?Quarter $2$ ?Quarter $3$ ?Quarter $4$

$20194,0874,4304,3586,537$

$20202,1603,2133,7795,879$

$20213,6624,2234,3666,220$

$20223,4714,0874,0525,775$

Source: Kohl $$ s $,$ ?Investor Relations

a $.$ ?Construct a graph of the series and describe the patterns you see.

b $.$ ?Forecast the four quarters of $2023$ ?using all appropriate forecasting models. Do not use any transformations $($ like logarithms $)$ ?even if you think one is necessary.

c $.$ ?Which model is best, and why? Include in your answer a comparison of the forecasts to actual sales in the first quarter of $2023,$ ?which was $ $3,355.$

$2.$ ?A small company has the technology to develop a product, but has concerns about its competition. They estimate that it will cost $ $670,000$ ?to develop and market the product. Analysts have projected revenues of $ $1\mathrm{.}2$ ?million if sales are high, $ $840,000$ ?if sales are moderate, and $ $440,000$ ?if sales are low. Alternatively, the company could do nothing. $(4$ ?points $)$

a $.$ ?Find EV and SD for the two actions $($ develop or not develop $),$ ?using probabilities of $0\mathrm{.}2$ ?for high sales, $0\mathrm{.}6$ ?for moderate sales, and $0\mathrm{.}2$ ?for low sales. Use a spreadsheet with formulas for your calculations and upload the spreadsheet into Moodle.

b $.$ ?What would you recommend to the company? Develop the product or not? Why? Put your answer to this question in your Word document.