Probability Distributions?

Question:

The mangmnt team recommends order quantities of 15,000, 18,000, 24,000, 28,000. Considerable disagreement concerning the market potential is evidenced by the different order quantities suggested. The product management team has asked you for an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation. Specialty expects to sell Weather Teddy for $24, and the cost is $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 similar products, Specialty's senior sales forecaster predicted an expected demand of 20,000 units with a 0.90 probability that demand would be between 10,000 units and 30,000 units.

2. Compute the projected profit for the order quantities suggested by the management team under 3 scenarios. Worst=10,000 units, most likely=20,000 units, best=30,000

Answer:
Hi,

15,000 units at a cost of $16/unit = $240,000 invested
Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income
Profit: $25,000
Most likely #sold: 15000 x 24 = $360,000 income (20,000 could have been sold, but sales were limited by order size)
Profit: $120,000
Best case #sold: 15000 x 24 = $360,000 income (30,000 could have been sold, but sales were limited by order size)
Profit: $120,000

18,000 units at a cost of $16/unit = $288,000 invested
Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income
Loss of -$23,000
Most likely #sold: 18000 x 24 = $432,000 income (20,000 could have been sold, but sales were limited by order size)
Profit: $144,000
Best case #sold: 18000 x 24 = $432,000 income (30,000 could have been sold, but sales were limited by order size)
Profit: $144,000

24,000 units at a cost of $16/unit = $384,000 invested
Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income
Loss of $119,000
Most likely #sold: 20000 x 24 + 4000 x 5 = $500,000 income Profit: $116,000
Best case #sold: 24000 x 24 = $576,000 income (30,000 could have been sold, but sales were limited by order size)
Profit: $192,000

28,000 units at a cost of $16/unit = $448,000 invested
Worst case #sold: 10000 x 24 + 5000 x 5 = $265,000 income
Loss of $183,000
Most likely #sold: 20000 x 24 + 4000 x 5 = $520,000 income
Profit: $72,000
Best case #sold: 28000 x 24 = $672,000 income (30,000 could have been sold, but sales were limited by order size)
Profit: $224,000

I hope that is what you wanted!! :-)

Probability Distributions?

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