Specialty

Chapter 6
Continuous Probability Distributions

Case Problem: Specialty Toys

1. Information provided by the forecaster

At x = 30,000,

[pic]

[pic]

Normal distribution [pic][pic]

2. @ 15,000

[pic]

P(stockout) = 0.3365 + 0.5000 = 0.8365

@ 18,000

[pic]

P(stockout) = 0.1517 + 0.5000 = 0.6517

@ 24,000[pic]

P(stockout) = 0.5000 - 0.2823 = 0.2177

@ 28,000

[pic]

P(stockout) = 0.5000 - 0.4418 = 0.0582

3. Profit projections for the order quantities under the 3scenarios are computed below:

Order Quantity: 15,000

| | |Sales | |
|Unit Sales |Total Cost |at $24|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

| | |Sales| |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |288,000 |240,000 |40,000 | -8,000|
|20,000 |288,000 |432,000 | 0 |144,000 |
|30,000 |288,000 |432,000 | 0 |144,000 |

OrderQuantity: 24,000

| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000|384,000 |240,000 |70,000 | -74,000 |
|20,000 |384,000 |480,000 |20,000 |116,000 |
|30,000 |384,000...