# Specialty Toys

Managerial Report for Specialty Toys
Thomas W Titus
Walsh University

Specialty Toys is faced with the decision of having to decide how many units of Weather Teddy should be purchased in order to meet the sales demand.   The company must decide on the best forecasted quantity so that market demand is able to be met without merchandise shortages but without purchasing too much of the product and risking excess inventory and consequently, reduced profits.   Management has recommended varying order quantities, or decision alternatives, of 15,000, 18,000, 24,000, and 28,000, indicating that there is a disagreement over what the market demand for Weather Teddy will be for the upcoming holiday season.   Each alternative needs to be measured against three possible scenarios for market demand; worst case of 10,000 units, most likely case of 20,000 units, and best case of 30,000 units.   Assuming a sales price of \$24 and a cost of \$16 for Weather Teddy, plus an inventory sales price of \$5, profit under each scenario will be calculated for each decision alternative.   Specialty’s Senior Forecasted has predicted that the average demand will be 20,000 units and is 95% confident that demand will be between 10,000 and 30,000 units.

Let X be the demand for the toy. Then X follows normal distribution with mean μ = 20000 and standard deviation σ.
Then P(10000 < X < 30000) = 0.95
P((10000-20000)/σ < (X-20000)/σ < (30000-20000)/σ) = 0.95
From tables of areas under the standard normal curve (30000-20000)/σ = 1.96
σ = (30000-20000)/1.96 =10000/1.96 = 5102
1. The demand distribution can be approximated by a normal distribution with mean µ = 20000 and standard deviation σ = 5102.

2. Probability of stock out with an order of K units is P(X > K) = P(Z > (K-20000)/5102), where Z is distributed as standard normal
Order (K) | (K-20000)/5102 | P(X > K) |
15000 | -0.98001 | 0.836458876 |
18000 | -0.392 | 0.652472052 |
24000 | 0.784006 |...