A Case Study of SuperFun Toys, Inc.
ACase Study of SuperFun Toys, Inc.
Institution’sName
ACase Study of SuperFun Toys, Inc.
SuperFunToys Inc. is involved with selling a wide range of original andinventive children`s toys. Its management has discovered that thetime before the December holiday season is the perfect period tolaunch new toys. To achieve this the company suggests thatmanufacturing of new toys should have commenced by June or July, andthen be ready to be transported to the supermarket shelves byOctober.
Inthis case study, I have been tasked with assisting SuperFun Toys Inc.in performing statistical analysis and profit projections to helpguide its plans of launching a new toy named Weather Teddy. This toyis made in Taiwan and is a weatherpredicting teddy bear. Theindepth analysis will give the company’s management the ability toview the probabilities of stockouts at different order quantities ofthe Weather Teddy, assessments of the toy’s profit potential, andalso give an optimum order quantity recommendation. The analysis willbe performed through the following three key questions:
Question1
Thedemand has a mean (μ) = 20,000 units. The mean is taken to be 20,000units because it is the number of sales at which SuperFun predictedwith a 95% possibility that the toys’ demand would range from10,000 to 30,000 units. Using M to be the customers’ demand for theWeather Teddy toy, and assuming Y follows a normal distribution. Itsstandard deviation is given by σ. It follows that:
Usingthe tables of areas under the standard normal distribution curveresults in:
=5,102
Thedata has distribution curve below showing a uniform distribution forthe various demands for the toy (15,000, 18,000, 20,000, 24,000, and28,000). Using the curve, the Empirical rule can be proven right. Therule has three conditions which have to be satisfied, the first ofwhich states that 68% of the data points should fall within 1standard deviation (Grimmett & Welsh, 2014). In this case, 80% ofthe data falls within 1 standard deviation. 28,000 is the only valuethat falls outside 1 standard deviation. All the other values fallwithin 2 and 3 standard deviations from the mean (the second andthird conditions indicate that 95% and 99.5% of data should fallwithin 2 and 3 standard deviations respectively) (Grimmett &Welsh, 2014)
Figure1:Normal distribution curve showing demand and the Empirical Rule
Question2
Themanagement team has put forward some stockout quantities. Thesequantities are 15,000, 18,000, 24,000 and 28,000. Using the mean fromabove (20,000), a standard deviation of 5,102, and T to represent theorder quantities, then the probabilities of stockouts occurring atthe stated quantities can be calculated using P (X > T) = P (Z >(Tmean/standard deviation)) (Grimmett & Welsh, 2014). Replacingwith the values of mean and the standard deviation the equationbecomes P (X > T) = P (Z > (T20,000/5,102)). Z is the zscoreand is a standard variable for normal distribution. For the differentvalues of T (order quantities) the probabilities are:
Order quantity (T) 
Z = (T – 20,000)/5,102 
Cumulative Probability, P(T) 
P(X >T) 
15,000 
0.98 
0.163543 
0.836457 
18,000 
0.392 
0.347529 
0.652471 
24,000 
0.784 
0.784652 
0.215348 
28,000 
1.568 
0.941559 
0.058441 
Thesecomputed probabilities indicate that the probability of a stockoutoccurring is the highest when the unit quantity is at 15,000 and islowest when the unit quantity is at 28,000. This suggests that thehigher the unit quantity the lower the probability of a stockoutoccurring. This means out all the four quantities given by themembers of management a unit quantity of 15,000 presents the highestprobability of a stockout occurring.
Question3
Asone of the company’s managers stated that the profit possible wasbig enough such that the quantity of orders ought to possess a 70%possibility of satisfying the demand then the quantity that can beordered in such a scenario can be computed by as follows:
First,we compute the order quantity (T) required to satisfy the 70% demandas shown below:
T= 20000 + (5102 * 0.5244)
T= 20000 + 2675
T= 22,675
Usingthis quantity of 22,675 units and the three case scenarios:

Pessimistic scenario (only 10,000 units are sold)

Likely scenario (only 20,000 units are sold)

Optimistic scenario (30,000 units are sold. In this case it means all of the 22,675 units are sold)
Thevalues below were computed using Microsoft Excel, and the Excel sheetincluded contains this information.

Unit Sales
Total Cost at $16/unit
Q = 22,675
Sales at $24/unit
Excess Inventory Sales at $5/unit
Profit
10,000
$362,800
$240,000
$0
$240,000
20,000
$362,800
$480,000
$13,375
$493,375
30,000
$362,800
$544,200
$0
$544,200
Accordingto the projected profits computed above the company will satisfy a70% demand from the customers by filling its inventory with 22,675units of Weather Teddies. This will also bring the company the mostprofits.
Conclusion
Accordingto the information in the Excel sheet included, the optimum orderquantity that can be ordered by the company’s management is 24,000units since it will bring in $576,000 in revenues and $192,000 inprofits using the “Likely” and the “Optimistic” scenarios.
References
Grimmett,G., & Welsh, D. (2014). Probability:An Introduction.Oxford: Oxford University Press.
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