  # Solution to Case Problem Specialty Toys

Topics: Standard deviation / Pages: 4 (761 words) / Published: Nov 28th, 2012
Solution to Case Problem Specialty Toys

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 |