SuperFun Toys Case Study

University of Phoenix

QNT/561 Applied Business Research & Statistics

**SuperFun**** Toys Case Study**

The members of the management team of SuperFun Toy have asked our team to perform statistical analysis and profit projection of a new product called Weather Teddy. The management team need this information to avoid purchasing too few or top many Weather Teddy which will case a lost in sales and reduction in profit. To give management the information they need for purchasing the new product, our team will need to use the sales forecaster’s prediction to describe a normal probability and sketch the distribution and show its means and standard deviation using the Empirical Rule. Computation for probability of a stock-out for orders quantities of 15,000, 18,000, 24,000, and 28,000 and computation for projected profit for order quantities of 10,000 units, 20,000 units, and 30,000 unites need to be done. Our team will also show what quantity would be ordered un the 70% chance of meeting demand and only 30% chance of any stock-outs.

**Normal Probability Distribution **

For SuperFun Toys, the empirical rule is the best route to calculate the demand distribution. This rule conveys that 68% of the information will fall inside one standard deviation of the mean, 95% of the information will fall inside two standard deviations of the mean, and practically all (99.7%) of the information will fall inside three standard deviations of the mean.

The empirical rule gauges the normality of the calculations. At the point when various information focuses fall outside the three standard deviation expectation, it can demonstrate non-ordinary distributions.

**Distribution Sketch Using the Empirical Rule**

SuperFun’s senior sales forecaster reviewed the sales history of similar product of their Weather Teddy and has predicted to expect a demand of 20,000 units with a 95% probability that demand would be between 10,000 units and 30,000 units. The empirical rule is divided into three standard deviations of three different percentages. The first standard deviation falls under 68%, the second standard deviation is under 95%, and the third is under 99.7%. The sketch provided in Figure 1 displays the mean and the standard deviation within the empirical rule. The mean for the SuperFun Toys is 20,000 and the standard deviation is 5,102 with the demand for Weather Teddy falls under the second standard deviation at 95%, which is outline in red on the sketch. Figure 1, illustrates the predication by the senior sales forecaster on the demand for 20,000 units with a 95% probability that demand would be between 10,000 units and 30,000 units is around a true population value.

**The Probability of a S****tock-out f****or Quantities**

According to Stockout, (2019), a stock out is “a situation in which the demand or requirement for an item cannot be fulfilled from the current inventory.” Determining the inventory level of a business so that the business will be able to maintain a profit is one of the most crucial challenges faced by management.

If the demand is, let’s say X and the Order Quantity is Q, then the Probability of a stock out would be

Order Quantity (K) | Z=(K−20,000)/5102 | P(Z | P(Stock Out) |
---|---|---|---|

15,000 | 0.98 | 0.1635 | 0.8365 |

18,000 | −0.39 | 0.3483 | 0.4517 |

24,000 | 0.78 | 0.7823 | 0.2177 |

28,000 | 1.57 | 0.9418 | 0.0582 |

**Projected Profit.**

- P(Stockout) = P(X>Q)
- =P(10,000>15,000)
- = P(Z>) where standard deviation is
- = P()
- X2 = 18,000 + 0.53(5102) = 20,704
- X3 = 20,000 + 0.53(5102) = 22,704

X4 = 24,000 + 0.53(5102) = 26,704 - X5 = 28,000 + 0.53(5102) = 30,704
**Projected Profit under the three scenarios**. **References**

Order Quantity | 15,000 | ||||||
---|---|---|---|---|---|---|---|

Purchase Cost per unit | $ 16.00 | ||||||

Sales | Order Quantity | Total Cost | Total Revenue | Profit | |||

@ $24.00 | @ $5.00 | ||||||

Pessimistic | 10,000 | 15,000 | $ 240,000 | $ 240,000 | $ 25,000 | $ 25,000 | |

Likely | 20,000 | 15,000 | $ 240,000 | $ 360,000 | $ 120,000 | ||

Optimistic | 30,000 | 15,000 | $ 240,000 | $ 360,000 | $ 120,000 | ||

Order Quantity | 18,000 | ||||||

Purchase Cost per unit | $ 16.00 | ||||||

Sales | Order Quantity | Total Cost | Total Revenue | Profit | |||

@ $24.00 | @ $5.00 | ||||||

Pessimistic | 10,000 | 18,000 | $ 288,000 | $ 240,000 | $ 40,000 | $ (8,000) | |

Likely | 20,000 | 18,000 | $ 288,000 | $ 432,000 | $ 144,000 | ||

Optimistic | 30,000 | 18,000 | $ 288,000 | $ 432,000 | $ 144,000 | ||

Order Quantity | 20,000 | ||||||

Purchase Cost per unit | $ 16.00 | ||||||

Sales | Order Quantity | Total Cost | Total Revenue | Profit | |||

@ $24.00 | @ $5.00 | ||||||

Pessimistic | 10,000 | 20,000 | $ 320,000 | $ 240,000 | $ 50,000 | $ (30,000) | |

Likely | 20,000 | 20,000 | $ 320,000 | $ 480,000 | $ 160,000 | ||

Optimistic | 30,000 | 20,000 | $ 320,000 | $ 480,000 | $ 160,000 | ||

Order Quantity | 24,000 | ||||||

Purchase Cost per unit | $ 16.00 | ||||||

Sales | Order Quantity | Total Cost | Total Revenue | Profit | |||

@ $24.00 | @ $5.00 | ||||||

Pessimistic | 10,000 | 24,000 | $ 384,000 | $ 240,000 | $ 70,000 | $ (74,000) | |

Likely | 20,000 | 24,000 | $ 384,000 | $ 480,000 | $ 20,000 | $ 116,000 | |

Optimistic | 30,000 | 24,000 | $ 384,000 | $ 576,000 | $ 192,000 | ||

Order Quantity | 28,000 | ||||||

Purchase Cost per unit | $ 16.00 | ||||||

Sales | Order Quantity | Total Cost | Total Revenue | Profit | |||

@ $24.00 | @ $5.00 | ||||||

Pessimistic | 10,000 | 28,000 | $ 448,000 | $ 240,000 | $ 90,000 | $ (118,000) | |

Likely | 20,000 | 28,000 | $ 448,000 | $ 480,000 | $ 40,000 | $ 72,000 | |

Optimistic | 30,000 | 28,000 | $ 448,000 | $ 672,000 | $ 224,000 |

**Quantity to be ordered under the new policy**.

We need to find the value of Z that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative distribution probability table, we find that z=0.53.

To find the quantity corresponding to z=0.53, we have

Z=x-u/sigma. Where x is the required quantity.

X1 = 15,000 + 0.53(5102) = 17,704

Sales | Order Quantity | Cost of Purchase | Total Revenue | Profit | |

Pessimistic | 10,000 | 17,704 | 283,264 | 240,000 | -43,264 |
---|---|---|---|---|---|

Most likely | 20,000 | 17,704 | 283,264 | 480,000 | 196,736 |

Optimistic | 30,000 | 17,704 | 283,264 | 720,000 | 436,736 |

Sales | Order Quantity | Cost of Purchase | Total Revenue | Profit | |

Pessimistic | 10,000 | 20,704 | 331,264 | 240,000 | -91,264 |
---|---|---|---|---|---|

Most likely | 20,000 | 20,704 | 331,264 | 480,000 | 148,736 |

Optimistic | 30,000 | 20,704 | 331,264 | 720,000 | 388,736 |

Sales | Order Quantity | Cost of Purchase | Total Revenue | Profit | |

Pessimistic | 10,000 | 22,704 | 363,264 | 240,000 | -123,264 |
---|---|---|---|---|---|

Most likely | 20,000 | 22,704 | 363,264 | 480,000 | 116,736 |

Optimistic | 30,000 | 22,704 | 363,264 | 720,000 | 356,736 |

Sales | Order Quantity | Cost of Purchase | Total Revenue | Profit | |

Pessimistic | 10,000 | 26,704 | 427,264 | 240,000 | -187,264 |
---|---|---|---|---|---|

Most likely | 20,000 | 26,704 | 427,264 | 480,000 | 52,736 |

Optimistic | 30,000 | 26,704 | 427,264 | 720,000 | 292,736 |

Sales | Order Quantity | Cost of Purchase | Total Revenue | Profit | |

Pessimistic | 10,000 | 30,704 | 491,264 | 240,000 | -251,264 |
---|---|---|---|---|---|

Most likely | 20,000 | 30,704 | 491,264 | 480,000 | -11,264 |

Optimistic | 30,000 | 30,704 | 491,264 | 720,000 | 228,736 |

**Recommendation**

After studying our analysis that we performed, the team has determined that in order for SuperFun Toys to order a new product without lost and sales and reduction in property, the recommended range of new products to be ordered should be between 20,000 and 25,000. It has also been determined that under the 70% chance of meeting demand and 30% chance of any stock-outs, the number of quantities that need to be ordered is around 23,000. Furthermore, we advise the company to carefully watch their level of demand so that the company will avoid over ordering quantities.

Black, K. (2017). Business Statistics: For Contemporary Decision Making, (9th ed). Hoboken, NJ: Wiley.

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