A Distributor Has Generated a Rough Estimate of Aftershave Demand $$\begin{array} { l | c c c c } \text { Demand } & 230 & 330 & 430 & 530 \\\hline \text { Weight } & 0.15 & 0.25 & 0.35 & 0.25\end{array}$$

question 41

Essay

A distributor has generated a rough estimate of aftershave demand at their retails store. The distributor is confident that demand will range from 100 to 650. The following table lists weights for demand values within this range.
​ $$\begin{array} { l | c c c c } \text { Demand } & 230 & 330 & 430 & 530 \\\hline \text { Weight } & 0.15 & 0.25 & 0.35 & 0.25\end{array}$$ ​
The distributor pays a wholesale price of $21 per aftershave and then sells at a retail price of $31.
​
a. Construct a spreadsheet model that computes net profit corresponding to a given level of demand and specified order quantity. Model demand as a random variable with ASP's custom general distribution.
b. Using simulation optimization, determine the order quantity that maximizes expected profit. What is the probability of running out of aftershave at this order quantity?
c. How many aftershaves does the distributor need to order so that the probability of running out of aftershaves is only 25 percent? How much expected profit will the distributor lose if he orders this amount rather than the amount from part b?

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Definitions:

Monopolistically Competitive

A market structure characterized by many sellers offering differentiated products, allowing some degree of pricing power and market segmentation.

AVC

Average Variable Cost (AVC) is the total variable costs of production divided by the quantity of output produced, representing the variable cost per unit.

ATC

Stands for Average Total Cost, which is the sum of all production costs divided by the quantity of output produced.

MR = MC

This key term signifies the point where Marginal Revenue (MR) equals Marginal Cost (MC), typically marking the profit-maximizing level of production for a firm.