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Running header: Specialty Toys: Case Study 1

Specialty Toys: Case Study Andrea Starkweather National American University MT4210 - Quantitative Analysis

Running header: Specialty Toys: Case Study 2 Abstract This paper will prepare a managerial report that addresses issues for the Weather Teddy product and also recommend an order quantity for the product.

Running header: Specialty Toys: Case Study 3 Specialty Toys: Case Study

1. Let X = the demand for the toy. X follows normal distribution with mean μ = 20000 and standard deviation σ. 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

Running header: Specialty Toys: Case Study 4 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 and z will be greater than K must be 1.000 – cumulative probability. P(X > K): 1- cumulative Order (K)

(K-20000)/5102 probability

15,000

-0.98001

18,000

-0.392

24,000

0.784006

28,000

1.568013

3. 15,000 units at a cost of $16/unit = $240,000 invested. a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 Profit: $25,000 b. Most likely #sold: 15000 x 24 = $360,000 income Profit: $120,000 c. Best case #sold: 15000 x 24 = $360,000 income Profit: $120,000 18,000 units at a cost of $16/unit = $288,000 invested a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income Loss of -$23,000 b. Most likely #sold: 18000 x 24 = $432,000 income Profit: $144,000 c. Best case #sold: 18000 x 24 = $432,000 income

0.836458876 0.652472052 0.216518215 0.058439102

Running header: Specialty Toys: Case Study 5 Profit: $144,000 24,000 units at a cost of $16/unit = $384,000 invested a. Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income Loss of $119,000 b. Most likely #sold: 20000 x 24 + 4000 x 5 = $500,000 income Profit: $116,000 c. Best case #sold: 24000 x 24 = $576,000 income Profit: $192,000 Order

Scenario 10000

Scenario 20000

15000 8*10000-11*5000 =25000 8*15000=120000 18000 8*10000-11*8000

Scenario 30000 8*15000 = 120000

8*18000 = 144000 8*18000 = 144000

= -8000 24000 8*10000-11*14000 = -74000 28000 8*10000-11*18000 = -118000

8*20000-11*4000

8*24000 = 192000

=116000 8*2000-11*8000

8*28000 = 224000

=72000

Cost of sales per unit $24 - Cost of goods sold $16 = profit per unit 8 Cost of sales per unit $24 – Cost of surplus inventory $5 – profit per $8 = coverage $11

4. The order quantity to meet 70% demand is found by solving P(X < K) =0.70 P (Z < (K-20000)/5102) = 0.70

Running header: Specialty Toys: Case Study 6 (K-20000)/5102 = 0.5244 K = 20000 + 5102 * 0.5244 = 20000 + 2675 = 22,675 units to be ordered. 5. The best case in which sales equals 30,000 units. Expected sales price = 22,675 * 24 = $544,200 The suggested order quantities is 22,675, so the cost price is 22,675*16 = $362,800 Sales is expected to be 30,000 so there is no stock out and The projected profit = sales price – cost price 544,200 – 362,800 = $181,400 The most likely case in which sales equal 20,000 units Expected sale price = 544,200 Cost is 22,675 * 16 = 362,800 There is no stock out Projected profit = 544,200 – 362,800 = $181,400 Worst case in which sales equal 10,000 units Sell for $24 based on cost of $16 per unit Expected sales = 10,000 * 24 = $240,000 Cost price is 22,675 * 16 = $362,800 Stock out is 22, 675 – 10,000 = 12,675 units. These will be sold at $5 per unit = 12,675 *5 = $63,375 Total sale price = 240,000 + 63,375 = $303,375 Projected profit = 362,800 – 303,375 = $59,425

Running header: Specialty Toys: Case Study 7 The best recommendation would be to order between 15,000 to 18,000 because even in the worst scenario, if the order quantity is 15,000 there will be profit of about $89,137.50 which puts you at the mid-range mark.

Running header: Specialty Toys: Case Study 8 References TalkStats, (2011). need-help-with-Case-problem-Specialty-Toys...pleasseeeee http://www.talkstats.com/showthread.php/4312-need-help-with-Case-problem-SpecialtyToys...pleasseeeee...