question archive The Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine

The Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine

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The Wine Company purchases grapes from one of two nearby 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 that will result in a percentage of bottles being used as fillers for cheaper table wines according to the following distribution.

 

Probability of % Defective

Percentage Defective

Grower A

Grower B

2

0.12

0.26

4

0.21

0.34

6

0.26

0.22

8

0.31

0.10

10

0.10

0.08

The two growers charge a different price for their grapes 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%

$44200

$42600

4%

$40200

$40300

6%

$36200

$38000

8%

$32200

$35700

10%

$28200

$33400

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

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