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Autor: people 10 August 2011
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1) Use the sales forecaster's prediction to describe a normal probability distribution that can be used to app the demand distribution. Sketch the distribution and show its mean and standard deviation. Solution: for finding the mean and standard deviation wish to use the following lines of case Specialty senior sales forecaster predicted an expected demand of 20000 units with a probability of 0.90 that the demand will between 10k and 30k. This tells that 90% confidence interval for this product is 20000+/10000 Consider that a 100(1a) % CI has the form mean +/ Z (a/2) S.D, there fore Value obtained is 1.645 Now we know that +/ 1.645 S.D from the mean contains 90% of value so we can get S.D Z=(Xmean/S.D) =1.645 S.D=Xmean/Z =30k20k/1.645 =6079 units so the distribution has mean=20k and S.D=6079 units. 2) Compute the probability of stockout for the order quantities suggested by members of Management team. a) For 15k Z=15k20k/6079= 0.8225 Now P (Z>0.8233) = 0.7939 Analysis: this tells that 79.39% chance for company to run out of weather teddy at 15k units. b) For 18k Z=18k20k/6079= 0.329 Now P (Z>0.329) = 0.6293 Analysis: this tells that 62.93% chance for company to run out of weather teddy at 18k units. c) For 24k Z=24k20k/6079= 0.658 Now P (Z> 0.658) = 0.2546 Analysis: this tells that 25.46% chance for company to run out of weather teddy at 24k units. d) For 28k Z=28k20k/6079=1.316 Now P (Z>1.317) = 0.0951 Analysis: this tells that 9.51% chance for company to run out of weather teddy at 28k units. 3) Compute the projected profit for the order quantities suggested by the management team under three Scenarios: worst case in which sales =10k units, most likely case in which sales=20k units and best case in which sales=30k units. Solution) Computation of Projected Profit: Worst Case scenario: Sales = 10,000 units Most Likely Case: Sales = 20000 units Best Case Scenario: Sales = 30000 units 4 order quantities suggested by the management: 15000 18000 24000 28000 a) Worst case: 1) 10k units with 15k units produced. Gross profit= 10k * $24 =$240000 Cost when 15k*$16=$240000 Remaining 5k units are sold at lower price 5k*$5=$25000 Profit in this case=$25000 2) 10k sold when 18k produced G/P=10k*$24=$240000 Cost when 18k*$16=$288000 Remaining 8k are sold at lower price 8k*$5=$40000 Loss will arise in this case for $8000 3)10k sold and 24k produced G/P=$240000 Cost when 24k*$16=$3 ...
