# Solution to Case Problem Specialty Toys

**Topics:**Standard deviation, Normal distribution, Variance

**Pages:**4 (761 words)

**Published:**November 28, 2012

10/24/2012

I. Introduction:

The Specialty Toys Company faces a challenge of deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales. Here, I will help to analyze an appropriate order quantity for the company. II. Data Analysis:

1.

20,0

00

.025

10,0

00

30,0

00

.025

.95

20,0

00

.025

10,0

00

30,0

00

.025

.95

Since the expected demand is 2000, thus, the mean µ is 2000. Through Excel, we get the z value given a 95% probability is 1.96. Thus, we have: z= (x-µ)/ σ=(30000-20000)/ σ=1.96, so we get the standard deviation σ=(30000-20000)/1.96=5102. The sketch of distribution is above. 95.4% of the values of a normal random variable are within plus or minus two standard deviations of its mean.

2. At order quantity of 15,000, z= (15000-20000)/5102=-0.98, P(stockout) = 0.3365 + 0.5 = 0.8365

At order quantity of 18,000, z= (18000-20000)/5102=-0.39,

P(stockout) = 0.1517 + 0.5= 0.6517

At order quantity of 24,000, z= (24000-20000)/5102=0.78,

P (stockout) = 0.5 - 0.2823 = 0.2177

At order quantity of 28,000, z= (28000-20000)/5102=1.57,

P (stockout) = 0.5 - 0.4418 = 0.0582

3.

Order Quantity = 15,000|

Unit Sales| Total Cost| Sales at $24| Sales at $5| Profit| 10,000| 240,000| 240,000| 25,000| 25,000|

20,000| 240,000| 360,000| 0| 120,000|

30,000| 240,000| 360,000| 0| 120,000|

Order Quantity = 18,000|

Unit Sales| Total Cost| Sales at $24| Sales at $5| Profit| 10,000| 288,000| 240,000| 40,000| -8000|

20,000| 288,000| 432,000| 0| 144,000|

30,000| 288,000| 432,000| 0| 144,000|

Order Quantity = 24,000|

Unit Sales| Total Cost| Sales at $24| Sales at $5| Profit| 10,000| 384,000| 240,000| 70,000| -74,000|

20,000| 384,000|...

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