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The Valley Wine Company purchases grapes from either of two nearby grape growers each season to produce a particular red wine. It purchases enough grapes to produce 3000 bottles of the wine. Each grower supplies a certain portion of poor quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines according to the following probability distribution.   Probability of Percent Defective Defective (%) Grower A Grower B 2 .15 .30 4 .20 .30 6 .25 .20 8 .30 .10 10 .10 .10 The two growers charge a different prices for their grapes and because of differences in taste, the company charges different prices for their wine depending on which grapes they use. The annual profit from the wine produced from each grower's grapes for each percentage defective is as follows.   PROFIT DEFECTIVE GROWER A GROWER B  2% $44,200 $42,600  4   40,200  40,300  6   36,200  38,000  8   32,200  35,700 10   28,200  33,400 Use decision-tree analysis to determine from which grower the company should purchase grapes.

The Valley Wine Company purchases grapes from either of two nearby grape growers each season to produce a particular red wine. It purchases enough grapes to produce 3000 bottles of the wine. Each grower supplies a certain portion of poor quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines according to the following probability distribution.   Probability of Percent Defective Defective (%) Grower A Grower B 2 .15 .30 4 .20 .30 6 .25 .20 8 .30 .10 10 .10 .10 The two growers charge a different prices for their grapes and because of differences in taste, the company charges different prices for their wine depending on which grapes they use. The annual profit from the wine produced from each grower's grapes for each percentage defective is as follows.   PROFIT DEFECTIVE GROWER A GROWER B  2% $44,200 $42,600  4   40,200  40,300  6   36,200  38,000  8   32,200  35,700 10   28,200  33,400 Use decision-tree analysis to determine from which grower the company should purchase grapes.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 30P
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The Valley Wine Company purchases grapes from either of two nearby grape growers each season to produce a particular red wine. It purchases enough grapes to produce 3000 bottles of the wine. Each grower supplies a certain portion of poor quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines according to the following probability distribution.

  Probability of Percent Defective
Defective (%) Grower A Grower B
2 .15 .30
4 .20 .30
6 .25 .20
8 .30 .10
10 .10 .10

The two growers charge a different prices for their grapes and because of differences in taste, the company charges different prices for their wine depending on which grapes they use. The annual profit from the wine produced from each grower's grapes for each percentage defective is as follows.

  PROFIT
DEFECTIVE GROWER A GROWER B
 2% $44,200 $42,600
 4   40,200  40,300
 6   36,200  38,000
 8   32,200  35,700
10   28,200  33,400

Use decision-tree analysis to determine from which grower the company should purchase grapes.

43. The Valley Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine. It purchases enough grapes to produce 3,000 bottles of the wine. Each grower supplies a certain portion of poor-quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines, according to the following probability distribution: Probability of Percentage Defective Defective (%) Grower A Grower B .15 .30 4 20 .30 6 25 .20 8 .30 .10 10 .10 .10 The two growers charge different prices for their grapes and, because of differences in taste, the company charges different prices for its wine, depending on which grapes it uses. Following is the annual profit from the wine produced from each grower's grapes for each percentage defective: Profit Defective (%) Grower A Grower B 467 / 866 roduction to Management Science, Ninth Edition $44,200 $42,600 4 40,200 40,300 36,200 38,000 32,200 35,700 10 28,200 33,400 Use decision tree analysis to determine from which grower the company should purchase grapes. 2.
Transcribed Image Text:43. The Valley Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine. It purchases enough grapes to produce 3,000 bottles of the wine. Each grower supplies a certain portion of poor-quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines, according to the following probability distribution: Probability of Percentage Defective Defective (%) Grower A Grower B .15 .30 4 20 .30 6 25 .20 8 .30 .10 10 .10 .10 The two growers charge different prices for their grapes and, because of differences in taste, the company charges different prices for its wine, depending on which grapes it uses. Following is the annual profit from the wine produced from each grower's grapes for each percentage defective: Profit Defective (%) Grower A Grower B 467 / 866 roduction to Management Science, Ninth Edition $44,200 $42,600 4 40,200 40,300 36,200 38,000 32,200 35,700 10 28,200 33,400 Use decision tree analysis to determine from which grower the company should purchase grapes. 2.
43. The Valley Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine. It purchases enough grapes to produce 3,000 bottles of the wine. Each grower supplies a certain portion of poor-quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines, according to the following probability distribution: Probability of Percentage Defective Defective (%) Grower A Grower B .15 .30 4 20 .30 6 25 .20 8 .30 .10 10 .10 .10 The two growers charge different prices for their grapes and, because of differences in taste, the company charges different prices for its wine, depending on which grapes it uses. Following is the annual profit from the wine produced from each grower's grapes for each percentage defective: Profit Defective (%) Grower A Grower B 467 / 866 roduction to Management Science, Ninth Edition $44,200 $42,600 4 40,200 40,300 36,200 38,000 32,200 35,700 10 28,200 33,400 Use decision tree analysis to determine from which grower the company should purchase grapes. 2.
Transcribed Image Text:43. The Valley Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine. It purchases enough grapes to produce 3,000 bottles of the wine. Each grower supplies a certain portion of poor-quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines, according to the following probability distribution: Probability of Percentage Defective Defective (%) Grower A Grower B .15 .30 4 20 .30 6 25 .20 8 .30 .10 10 .10 .10 The two growers charge different prices for their grapes and, because of differences in taste, the company charges different prices for its wine, depending on which grapes it uses. Following is the annual profit from the wine produced from each grower's grapes for each percentage defective: Profit Defective (%) Grower A Grower B 467 / 866 roduction to Management Science, Ninth Edition $44,200 $42,600 4 40,200 40,300 36,200 38,000 32,200 35,700 10 28,200 33,400 Use decision tree analysis to determine from which grower the company should purchase grapes. 2.
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