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 ofPercent DefectiveDefective (%)Grower AGrower B2.15.304.20.306.25.208.30.1010.10.10The 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. PROFITDEFECTIVEGROWER AGROWER B 2%$44,200$42,600 4 40,200 40,300 6 36,200 38,000 8 32,200 35,70010 28,200 33,400Use decision-tree analysis to determine from which grower the company should purchase grapes. # Analyzing Grape Purchase Decisions for Wine Production**Problem Context:**The Valley Wine Company sources grapes from two nearby growers each season to produce a specific red wine. They buy enough grapes to make 3,000 bottles. The quality varies, leading to a certain percentage of defective grapes from each grower. These are utilized for lower-tier table wines. The company analyzes the probability distribution of defective grapes to determine optimal purchasing strategies.## Probability Distribution of Defective Grapes| Defective (%) | Grower A | Grower B ||---------------|----------|----------|| 2 | 0.15 | 0.30 || 4 | 0.20 | 0.30 || 6 | 0.25 | 0.20 || 8 | 0.30 | 0.10 || 10 | 0.10 | 0.10 |- **Grower A** has the highest probabilities of producing 8% defective grapes. - **Grower B** shows a higher likelihood of producing lower defective percentages early on (2% and 4%).## Profit Analysis Based on Defective Grapes| Defective (%) | Grower A Profit | Grower B Profit ||---------------|-----------------|-----------------|| 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 |- Profit declines as the percentage of defective grapes increases.- **Grower A** delivers higher profits when defect rates are low (2%).- **Grower B** becomes more profitable when defect rates are higher (8% and 10%).**Decision Consideration:**To optimize profits and quality, the Valley Wine Company should employ decision tree analysis to decide which grower to purchase grapes from. This involves evaluating probabilities and profit outcomes for strategic decision-making. # The Valley Wine Company Grape Purchase Analysis### IntroductionThe Valley Wine Company purchases grapes from one of two nearby growers each season to produce a particular red wine. The company buys enough grapes to produce 3,000 bottles of wine. Each grower supplies a certain portion of poor-quality grapes, affecting the percentage of bottles used as fillers for cheaper table wines. The following is a probability distribution of defective percentages from each grower.### Probability of Percentage Defective| Defective (%) | Grower A | Grower B ||---------------|----------|----------|| 2 | 0.15 | 0.30 || 4 | 0.20 | 0.30 || 6 | 0.25 | 0.20 || 8 | 0.30 | 0.10 || 10 | 0.10 | 0.10 |### Analysis of Profit Based on Percentage DefectiveThe two growers charge different prices for their grapes. Due to taste differences, the company adjusts wine prices according to the grapes used. Below is the annual profit from the wine produced with each grower's grapes for each percentage defective:| Defective (%) | Profit (Grower A) | Profit (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 |### Decision AnalysisTo determine the optimal grower for grape purchases, use decision tree analysis. This method will help assess the probabilities and corresponding profits, leading to a data-driven decision regarding which grower the company should choose for purchasing grapes.This decision process would involve calculating the expected monetary value (EMV) for each grower scenario based on defect percentages and associated profits. Consideration of both profitability and defect risk will be essential for maximizing the company’s returns.

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Answered: The Valley Wine Company purchases…

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...