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Autor: people • August 10, 2011 • Essay • 1,360 Words (6 Pages) • 1,600 Views
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(1-a) % 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
=6079 units so the distribution has mean=20k and S.D=6079 units.
2) Compute the probability of stock-out for the order quantities suggested by members of Management team.
a) For 15k
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
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
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
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:
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
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
Cost when 24k*$16=$384000
Remaining are sold at lower price 14k*$5=$70000
Loss will arise in this case for $74000
4) 10k sold and 28k produced
Cost when 28k*16=$448000
Remaining are sold at lower price 18k*$5=$90000
Loss will arise in this case for $118000
b) Most likely case: 1) 20k units produced 15k
Here we get profit of $120000
2) 20k units when 18k produced
Here profit is $$144000
3) 20k Demand 24k produced
Remaining are sold at lower cost 4k*$5=$20000
Here profit is $116000
4) 20k demand and 28k produced
Remaining goods are sold at lower cost 8k*$5=$40000
Here we get a profit of $72000
c) Best case: 1) 30k units demand and 15k produced
Here we get a profit of $120000
2) 30k demand and 18k produced
Here profit is $144000
3) 30k demand and 24k produced
Here profit is $192000