Specality Toys Case

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

Z=(X-mean/S.D) =1.645

S.D=X-mean/Z

=30k-20k/1.645

=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

Z=15k-20k/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=18k-20k/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=24k-20k/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=28k-20k/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=$384000

Remaining are sold at lower price 14k*$5=$70000

Loss will arise in this case for $74000

4) 10k sold and 28k produced

G/P=$240000

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

G/P=15k*$24=$360000

Cost=15k*$16=$240000

Here we get profit of $120000

2) 20k units when 18k produced

G/P=18k*$24=$432000

Cost=18k*$16=$288000

Here profit is $$144000

3) 20k Demand 24k produced

G/P=20k*$24=$480000

Cost=24k*$16=$384000

Remaining are sold at lower cost 4k*$5=$20000

Here profit is $116000

4) 20k demand and 28k produced

G/P=$480000

Cost=28k*$16=$448000

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

G/P=15k*$24=$360000

Cost=15k*$16=$240000

Here we get a profit of $120000

2) 30k demand and 18k produced

G/P=18k*$24=$432000

Cost=18k*$16=$288000

Here profit is $144000

3) 30k demand and 24k produced

G/P=24k*$24=$576000

Cost=24k*$16=$384000

Here profit is $192000

4)