Specialty Toys Demand Distribution
Essay by Swarna Manjari • October 26, 2018 • Case Study • 1,488 Words (6 Pages) • 759 Views
- Case study “Specialty Toys”
Question 1: Use the sales forecaster’s predictions to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its means and standard deviation.
Answer: According to the senior sales forecaster, there is an expected demand of 20,000 units with a 95% probability between 10,000 and 30,000 units.
Mean, µ = (10,000+30,000)/2
µ = 20,000
Since there is in an indication of 95% probability, the normal distribution chart (68-95-99.7 Rule) was used and the standard deviation was calculated as below,
µ+2σ ≈ 0.95
20,000+2σ ≈ 0.95
σ ≈ 5000
The normal distribution chart for this case is shown below in the figure.
[pic 1]
Question 2: Compute the probability of a stock-out for the order quantities suggested by members of the management team.
Answer: The recommended quantities by the management team were – 15,000, 18,000, 24,000 and 28,000. The mean and standard deviation calculated above were used to calculate the Z score. Using the table for the cumulative probabilities for the standard normal distribution, the respective probabilities were estimated. Estimation of the probability of a stock-out the was done as shown below,
X | µ | σ | Z | Prob(Z) | 1-Prob(Z) |
15,000 | 20,000 | 5,000 | -1 | 0.1587 | 0.8413 |
18,000 | 20,000 | 5,000 | -0.4 | 0.3446 | 0.6554 |
24,000 | 20,000 | 5,000 | 0.8 | 0.7881 | 0.2119 |
28,000 | 20,000 | 5,000 | 1.6 | 0.9452 | 0.0548 |
(Probability, in this case, can also be done using the excel function NORM.DIST(X, mean, standard_dev, cumulative))
Question 3: Compute the projected profit for the order quantities suggested by the management team under three scenarios - worst case: sales 10,000 units, most likely case: sales = 20,000 units, and best case: sales = 30,000 units.
Answer: The profit projected for the 3 scenarios can be seen below tables. Two conditions were used in the calculations - If the number of units in the case is less than the scenario’s units, then the remaining units were sold at a clearance price of $5 per unit otherwise all available units were sold at the selling price. The selling price and cost per unit are $24 and $16 respectively.
Case 1: 15,000 units
Scenario | Sale Units | Selling Price | Clearance Price | Revenue | Cost | Total Cost | Profit |
Worst Case | 10,000 | 24 | 5 | 265,000 | 16 | 240,000 | 25,000 |
Most Likely Case | 20,000 | 24 | 5 | 360,000 | 16 | 240,000 | 120,000 |
Best Case | 30,000 | 24 | 5 | 360,000 | 16 | 240,000 | 120,000 |
Case 2: 18,000 units
Scenario | Sale Units | Selling Price | Clearance | Revenue | Cost | Total Cost | Profit |
Worst Case | 10,000 | 24 | 5 | 280,000 | 16 | 288,000 | (8,000) |
Most Likely Case | 20,000 | 24 | 5 | 432,000 | 16 | 288,000 | 144,000 |
Best Case | 30,000 | 24 | 5 | 432,000 | 16 | 288,000 | 144,000 |
Case 3: 24,000 units
Scenario | Sale Units | Selling Price | Clearance | Revenue | Cost | Total Cost | Profit |
Worst Case | 10,000 | 24 | 5 | 310,000 | 16 | 384,000 | (74,000) |
Most Likely Case | 20,000 | 24 | 5 | 500,000 | 16 | 384,000 | 116,000 |
Best Case | 30,000 | 24 | 5 | 576,000 | 16 | 384,000 | 192,000 |
Case 4: 28,000 units
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