The Following Time Series Shows the Sales of a Particular

question 46

Essay

The following time series shows the sales of a particular commodity over the past 15 weeks. $$\begin{array} { | c | c | } \hline \text { Week } & \text { Sales } \\\hline 1 & 1,123 \\\hline 2 & 1,157 \\\hline 3 & 1,138 \\\hline 4 & 1,120 \\\hline 5 & 1,130 \\\hline 6 & 1,132 \\\hline 7 & 1,188 \\\hline 8 & 1,151 \\\hline 9 & 1,129 \\\hline 10 & 1,118 \\\hline 11 & 1,125 \\\hline 12 & 1,147 \\\hline 13 & 1,162 \\\hline 14 & 1,190 \\\hline 15 & 1,137 \\\hline\end{array}$$
a. Construct a time series plot. What type of pattern exists in the data?
b. Use α = 0.3 to develop the exponential smoothing values for the time series and compute the forecast of demand for the next week.
c. Use trial and error to find a value of the exponential smoothing coefficient α that results in a relatively small MSE.

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Definitions:

Total Revenue

The total amount of money received by a firm from the sale of goods or services before any costs or expenses are subtracted.

Average Variable Cost

The total variable costs (costs that change with production volume) divided by the number of units produced, representing the variable cost per unit.

Marginal Cost (MC)

Marginal Cost, abbreviated as MC, refers to the increase in total production cost that arises from producing an additional unit of output, emphasizing the concept of optimizing production levels.

Average Total Cost (ATC)

The total cost divided by the quantity of output produced, representing the per-unit cost of production.