# Ski Jacket

The analysis conducted shows the importance of quantity production variability on the profit maximizing verge.A range of values is presented by four Regional Sales Managers; each region includes the minimum, most likely and maximum sales values of a random variable.The sample data is described as simple, limited, and somewhat scarce; therefore, given the grade of uncertainty, the most appropriate and suitable distribution to use is the Triangular distribution.

**Ski Jacket**

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The Monte Carlo Simulation from Microsoft Excel @Risk, will calculate “a model output value many times with different input values.

The purpose is to get a complete range of all possible scenerios. ”1 For the Region 1 the demand is generated from (3000, 4000, 8000) with a mean of 5000. One point of interest in the data is the variability of the values. According to the parameters of this data the coefficient of variability is 22%. The graph is right skewed, as we see the mean (5000) is right to the median (4875), and the median is right to the mode (4000); its peak represents the most likely value (4000). According to the input the total demand average generated for this region is 5000 jackets.

For the Region 2 the demand is generated from (2000, 4000, 5000) with a mean of 3667. One point of interest in the data is the variability of the values. According to the parameters of this data the coefficient of variability is 17%. The graph is left skewed, as we see the mean (3667) is relatively close, but left to the median (3717), and the median is also close, and left to the mode (4013); its peak represents the most likely value (4000). According to the input the total demand average generated for this region is 3667 jackets.

For the Region 3 the demand is generated from (1500, 2000, 3500) with a mean of 2333. One point of interest in the data is the variability of the values. According to the parameters of this data the coefficient of variability is 18%. The graph is left skewed, as we see the mean (2,333) is left to the median (2269), and the median left to the mode (2242); its peak represents the most likely value (2000). According to the input the total demand average generated for this region is 2333 jackets. For the Region 4 the demand is generated from (500, 1000, 1500) with a mean of 1000.

One point of interest in the data is the variability of the values. According to the parameters of this data the coefficient of variability is 20%. The graph perfectly symmetric, the peak represents the most likely value (1000). According to the input the total demand average generated for this region is 1000 jackets. When the four Regional demands are summarize (5000, 3667, 2333, 1000) we totalize an estimate value of 12000 jackets. The four Regions have different means, standard deviation; the tendencies of the values are they decrease from Region 1 to Region 4. Beside the values provided by the four Regional Sales Managers, 12 Egress employees have independently estimated demand for the upcoming season. Using the same program described above, the sample data generated a mean of 11750, standard deviation 3678, and an IQR of 5039. The best distribution fit for the sample appears to be triangular. If compared to the Regional Manager’s demand, the mean generated from the employees’ estimate (11750) is very close to the total demand estimated by the triangular distribution (12000) from the manager’s data.

The most appealing option, between the two demand estimates, is the Regional Manager’s demand as it leads to the possibility of generating triangular distribution estimates, easy to understand and visualize any effect of any changes, which will result in positive decision making. There are three different quantities of production levels projected for the upcoming season (7800, 12000, 14000). According to the previous demand estimates, the total quantity demanded is 12000.

Therefore, the production level of 7800 jackets does not match the demand estimated; there is a demand shortage of 4200 jackets, which will result in disadvantage, explained as follows. When compared this quantity level of production with the 12000 production level, there is an $84,000 profit difference between both levels, which makes us determine that between both the most appealing alternative for profit maximization is the 12000 production level. On the other hand, the 14000 production level generated a total profit estimate of $40,000; his amount can be translated into a loss of $100,000 when compared to the 12000 production level. Meaning that, 2000 extra jackets produced over the estimated demand will be sold at $30 per unit instead of $100. However, if these 2000 extra jackets were to be sold at full price ($100 per unit) profits would increase by $40,000. Finally, when comparing all three production levels, we can conclude that the most suitable alternative, that comprises the most benefits, in terms of profit maximization, is the 12000 quantity production level.