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Pentryn Fruit Company cans and sells both fruit and vegetables. They are a medium sized company selling their product in the Midwest.
Ms. Mary Gordon, VP of Operations, is meeting with the Controller, the Sales Manager, and the Production Manager to discuss the amount of tomato products to can that season. The tomato crop, which was purchased at the start of the season, has ripened and is starting to arrive at their factory to be processed into three products, whole tomatoes, juice, and paste.
William Cooper, the Controller, Cindy Myers, the Sales Manager, arrived first. They were followed by Dan Tucker, the Production Manager. He had picked up Produce Inspection’s latest estimate of the quality of the incoming tomatoes. The report said that 20% of the crop was grade A and the rest of the 3,000,000-pound crop was Grade B.
Gordon asked Myers for her forecast of demand for tomato products for the coming year. She said they could sell all of the whole canned tomatoes they could produce. The expected demand for tomato juice and tomato paste was limited. She passed around her forecast, shown in Table 1. Selling prices had been set by upper management and it was based on cost, brand image, market penetration, and desired profit.
Cooper was pleased with the information and reminded the group about some facts related to their decision
• The new accounting system allowed him to determine the contribution of each product,
• The incremental profit on whole tomatoes was greater than juice and paste,
• Penryn had signed contracts with the growers in May, the average purchase price was $.12 per pound. Contribution is shown in Table 2
Tucker pointed out that although there was ample production capacity, it was impossible to produce all whole tomatoes because too small a portion of the tomato crop was Grade A. Penryn used a numerical scale to grade the quality of raw produce and prepared product. The scale was from 1 to 10 and had the following ratings
• Grade A tomatoes scored an average of 9
• Grade B tomatoes scored an average of 5
• The minimum average rating for whole tomatoes was 8
• The minimum average rating for juice was 6
• Paste could be made entirely from any grade tomato
• This limited whole tomato production to 800,000
Gordon has been able to find a source of more Grade A tomatoes at $.085 per pound. That offer was “still on the table.”
Myers expressed the opinion that the company will do well, but not by canning whole tomatoes. It was Myers opinion that tomato cost should be allocated based on quality and quantity, not just on quantity as Cooper had done. Therefore, Myers had recomputed the marginal profit on this bases (Table 3). She further recommended the following:
• 2000000 pounds of Grade B tomatoes for paste
• The remaining 400000 pounds of Grade B tomatoes and all of the Grade A tomatoes for juice
Analyze the problem, set it up and analyze it as a linear programming problem and write a memo detailing all of the particulars of your analysis and recommendations. You are all analysts for Lyth, Inc., that world famous management science consulting firm. Make sure you address the following questions and use the data shown based on your WIN
1. What is management’s objective and why?
2. What does management need to know?
3. What are the constraints?
4. What is your recommendation to Pentryn Fuit Company?
5. How much of each product should be made
a. Whole tomatoes
b. Juice
c. Paste
6. Should they buy the extra tomatoes?
7. Are there any leftover tomatoes? What grade?
8. How much would the pay for 1 additional pound of Grade A tomatoes?
Table 1 Demand forecast

If WIN is even If WIN is odd
Product Description Selling price Demand forecast Selling price Demand forecast
24-2 1/2 whole tomatoes $ 16.00 880000 16.38 720000
24-2 1/2 choice peach halves $ 21.60 11000 22.68 9000
24-2 1/2 peach nectar $ 18.40 5500 19.32 4500
24-2 1/2 tomato juice $ 18.00 55000 18.9 45000
24-2 1/2 cooking apples $ 19.60 16500 20.58 13500
24-2 1/2 tomato paste $ 15.20 88000 15.96 7200

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