Thread: need help with Case problem:Specialty Toys...pleasseeeee

1. need help with Case problem:Specialty Toys...pleasseeeee

some1 posted this ? awhile back but never received replies so maybe some1 can help me....ANY help is highly appreciated..heres the problem:

Members of a management team suggested order quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. the product management team asks you for an analysis of the stock-out probabilites for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation. Specialty (the company name) expects to sell Weather Teddy (the product) for \$24 based on a cost of \$16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventory for \$5 per unit. After reviewing the sales history of similiar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with a 0.95 probability that demand would be between 10,000 units and 30,000 units.

1. Use the sales forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.

2. Compute the probability of a stock-out for the order quantities suggested by members of the management team.

3. Compute the projected profit for the rder quantities suggested by the management team under three scenarios: worst case in which sales = 10,000 units, most likely case in which sales = 20,000 units, and best case in which sales = 30,000 units.

4. One of Specialty's managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What quantity would be ordered under this policy, and what is that projected profit under the three sales scenarios.

5. Provide your own recommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.

**i've gone thru the book & canNOT find a good example of this problem,mainly because each directly provide the mean & standard deviation.

-for starters,would the mean for #1 be 20,000 (therefore in the middle of the bell curve)?

-on #2,obv. we use the #s 15,000 18,000 24,000 28,000 but what else is needed

2. Originally Posted by paris playa69
-for starters,would the mean for #1 be 20,000 (therefore in the middle of the bell curve)?
To find the mean and standard deviation, use this statement from the problem:

Specialty's senior sales forecaster predicted an expected demand of 20,000 units with a 0.95 probability that demand would be between 10,000 units and 30,000 units.

This is saying that the 95% confidence interval for this product is 20,000 +/- 10,000.

Considering that a 100(1-a)% CI has the form mean +/- z[a/2]*sd, you can pick out what "mean" is in your problem, and determine sd (the standard deviation) using z[a/2] = z[.025] = 1.96

Originally Posted by paris playa69
-on #2,obv. we use the #s 15,000 18,000 24,000 28,000 but what else is needed
Let X = # of toys sold.
In the case where 15,000 (or any quantity Q) are shipped,
P[stock-out] = P[X > 15,000]
Since X is assumed to be normal, next you'll want to standardize X, and then do that stuff with the z-values.
=P[ Z > (15,000 - mean)/sd ] = 1 - Phi( (15,000-mean)/sd )

3. need help also

I desperately need advice on number four. How is the quantity that should be ordered computed? Im thinking its by using the Z score associated with 70% but im unsure. Does anyone know?

4. bump.
I don't understand what to do in number 2 and number 4.

-Matt

5. Let's assume that the expected sales distribution is normally distributed, with a mean of 20,000, and 95% falling within 10,000 and 20,000.

We need the standard deviation.

We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by:

z = (x - mu)/sigma = 1.96
sigma = (x - mu)/z

Sigma = (30,000-20,000) / 1.96 = 5,102 units.

So, we have a distribution with a mean of 20,000 and a standard deviation of 5,102.

#2 For each member's prediction, what is the probability that the quantities sold will be greater than their suggested order size? Find the z-score corresponding to the order size, and then find the tail area above.

#4 Find the value that has 70% area below it.

6. Re: need help with Case problem:Specialty Toys...pleasseeeee

Can someone please explain how to get to answers to #2 and #4 a little more?

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