Specialty Toys

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Specialty Toys Case Study

1. The mean is 20,000 units and there is a 95% probability that demand will be between 10, 000 and 30,000 units. This means there is a .025% chance that the demand will be outside of 10,000 and 30,000. Using the chart, we find that z=-1.96. Using the following calculation, we find:

z= x- μ

σ

-1.96 = 10,000 – 20,000

σ

σ=5102

Standard deviation σ = 5,102

μ = 20,000

mean

2. Stock outs were calculated by the four management numbers.

Equation is: z = (x – μ)/ σ

15,000:

Z = (15,000-20,000)/5102

z = -0.98

Then, reference the cumulative probabilities for standard deviation table in the beginning of the book to identify what -0.98 represents, which is .1635. Since stock outs are any quantity greater than what management suggested, they need to be subtracted from 1.

1 - .1635 = .8365 which

= 83.65%

Same logic/steps for the rest of the values:

18,000 24,000 28,000

Z = (18,000-20,000)/5102 z=(24,000-20,000)/5102 z=(28,000-20,000)/5102

z = -.39 z=.78 z= 1.57

1 - .3483 = .6517 1 - .7823 = .2177 1 –.9418 = .0582

which = 65.17% which = 21.77% which = 5.82%

3. Projected Profit for management under three scenarios which are 10,000 20,000 and 30,000 units

Order | 10,000 units | 20,000 units | 30,000 units |

15000 | 8*10000-11*5000 =\$25000 | 8*15000=\$120000 | 8*15000 = \$120000 |

18000 | 8*10000-11*8000= \$-8000 | 8*18000 = \$144000 | 8*18000 = \$144000 |

24000 | 8*10000-11*14000=...

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