Probability Analysis Paper 1

1

Philip Enterprises, distributor of video discs, is developing its budgeted cost of goods sold for next year. Philip has developed the following range of sales estimates and associated probabilities for the year:
Sales Estimate ..Probability
$ 60,000 ............25%
85,000 ...............40
100,000 .............35
Philip’s cost of goods sold averages 80% of sales. What is the expected value of Philip’s budgeted cost of goods sold?






2

The probabilities shown in the table below represent the estimate of sales for a new product.
Sales (Units).. Probability
0-200 .................15%
201-400............. 45%
401-600 .............25%
601-800............. 15%
What is the best estimate of the expected sales of the new product?






3

A beverage stand can sell either soft drinks or coffee on any given day. If the stand sells soft Fact Pattern:drinks and the weather is hot, it will make $2,500; if the weather is cold, the profit will be $1,000. If the stand sells coffee and the weather is hot, it will make $1,900; if the weather is cold, the profit will be $2,000. The probability of cold weather on a given day at this time is 60% Question: 962 The expected payoff for selling coffee is






4

A beverage stand can sell either soft drinks or coffee on any given day. If the stand sells soft Fact Pattern:drinks and the weather is hot, it will make $2,500; if the weather is cold, the profit will be $1,000. If the stand sells coffee and the weather is hot, it will make $1,900; if the weather is cold, the profit will be $2,000. The probability of cold weather on a given day at this time is 60%. The expected payoff if the vendor has perfect information is






5

A beverage stand can sell either soft drinks or coffee on any given day. If the stand sells soft Fact Pattern:drinks and the weather is hot, it will make $2,500; if the weather is cold, the profit will be $1,000. If the stand sells coffee and the weather is hot, it will make $1,900; if the weather is cold, the profit will be $2,000. The probability of cold weather on a given day at this time is 60%. If the probability of hot weather, given a hot weather forecast, is 50%, how much would the vendor be willing to pay for the forecast?






6

Under favorable weather conditions, the management of Flesher Farms expects its raspberry crop to have a $120,000 market value. An unprotected crop subject to frost has an expected market value of $80,000. If Flesher protects the raspberries against frost, the market value of the crop is still expected to be $120,000 under frost-free conditions and $180,000 if a frost occurs. What must be the probability of a frost for Flesher to be indifferent to spending $20,000 for tents to provide frost protection?






7


The College Honor Society sells hot pretzels at the home football games. The pretzels are sold for $1.00 each, and the cost per pretzel is $.30. Any unsold pretzels are discarded because they will be stale before the next home game. The frequency distribution of the demand for pretzels per game is presented as follows:
Unit Sales Volume Probability
2,000 pretzels 0.1
3,000 pretzels 0.15
4,000 pretzels 0.2
5,000 pretzels 0.35
6,000 pretzels 0.2
The estimated demand for pretzels at the next home football game using a deterministic approach based on the most likely outcome is






8


The College Honor Society sells hot pretzels at the home football games. The pretzels are sold for $1.00 each, and the cost per pretzel is $.30. Any unsold pretzels are discarded because they will be stale before the next home game. The frequency distribution of the demand for pretzels per game is presented as follows:
Unit Sales Volume Probability
2,000 pretzels 0.1
3,000 pretzels 0.15
4,000 pretzels 0.2
5,000 pretzels 0.35
6,000 pretzels 0.2
The conditional profit per game of having 4,000 pretzels available but only selling 3,000 pretzels is






9


The College Honor Society sells hot pretzels at the home football games. The pretzels are sold for $1.00 each, and the cost per pretzel is $.30. Any unsold pretzels are discarded because they will be stale before the next home game. The frequency distribution of the demand for pretzels per game is presented as follows:
Unit Sales Volume Probability
2,000 pretzels 0.1
3,000 pretzels 0.15
4,000 pretzels 0.2
5,000 pretzels 0.35
6,000 pretzels 0.2
The conditional profit per game of having 4,000 pretzels available and selling all 4,000 pretzels is






10

Alsen Company is in the process of preparing its budget. As part of the process, the company has prepared sales estimates and estimated the probability associated with each sales estimate. Which one of the following techniques should be used by Alsen to determine sales for budgeting purposes?






Result

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