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To advance the linear programming model that maximizes the net profit.

Roundtree Cannery is a medium sized company which produces as well as distributes a variety of fruit and vegetable products under private brands in the north-central states.  On Monday, September 14, 2009, Mr. Jackson, Vice-President of Operations, asked Ms. Adams, Controller, Mr. Owens, Vice President of Marketing, and Ms. Brandon, Vice President of Production, to see with him to discuss the amount of cranberry products to pack this season. The cranberry crop, which had been purchased at planting was beginning to arrive at the plant as well as packing operations would have to be started by the following Monday. A total of 3,000,000 pounds had been purchased. Assume no waste.

At the meeting each person was given the Produce Inspection Report that contained the latest estimate of the quality of incoming cranberries.  Interpretation to this report about 20% of the crop will be Grade a quality and the residual portion will be Grade B.  Mr. Jackson asked Mr. Owens about the appraised demand for cranberry products for the coming year.  Mr. Owens passed around the latest demand forecast (Exhibit 1-- Demand Forecasts: case selling price and number of cases demanded).  While the forecast designated that they could sell all of the whole canned cranberries they could produce the expected demand for cranberry juice as well as jellied cranberry was limited.  He prompted the group that the selling prices had been set in light of the long-term marketing strategy of the company as well as that the potential sales had been forecasted at these prices.

Exhibit 1

Demand Forecasts


Selling Price per Case

Demand Forecast (Cases)

24 packages/case whole cranberries



24 cans/case choice peach halves



24 cans/case peach nectar



24 bottles/case cranberry juice



24 can/case cooking apples



24 cans/case jelled cranberry sauce



Ms. Adams, after observing at the demand estimates said that it appeared like the company must do quite well on the cranberry crop this year. With the fresh accounting system that had been set up she had been able to find out the contribution for each product and according to her analysis, the incremental contribution on whole cranberries was greater than the incremental contribution on any other cranberry product. In May after Roundtree had hired contracts agreeing to purchase the grower=s production at an average delivered price of 6 cents per pound, Ms. Adams had find outd the cranberry products= contributions shown in Exhibit 2 (Product Item Profitability by Case). Exhibit 2 was dispersed to the officers at the meeting.

Exhibit 2

Product Item Profitability/Case


Whole cranberries

Peach halves

Peach nectar

Cranberry juice

Cooking apples

Cranberry jellied


Selling Price







Variable costs

Direct Labor







Variable Overhead







Variable selling cost







Packaging Material














Total Variable Costs














Less allocated overhead







Net profit







Product usage in terms of pounds per case is shown in Exhibit 3.

Exhibit 3. Product Usage


Pounds per Case

Whole cranberries


peach halves


Peach nectar


Cranberry juice


Cooking apples


Jellied cranberry sauce


Ms. Brandon transported to their attention that although there was ample production capacity, it was incredible to produce all whole cranberries since too small a portion of the cranberry crop was AA@ quality.  Roundtree utilized a numerical scale to record the quality of both raw products and prepared products.  This measure ran from zero to ten the higher number representing better quality.  As-per to this scale AA@ cranberries average nine points per pound and AB@ cranberries average five points per pound.  Ms. Brandon renowned that the minimum average input quality was eight points per pound for whole cranberries and six points per pound for juice.  Jellied cranberries could be made entirely from AB@ cranberries.  This meant which the whole cranberry production was limited to 800,000 pounds.

 Mr. Jackson stated that this wasn't a real limitation.  He had remained recently solicited to purchase 80,000 pounds of Grade a cranberries at $.085 per pound and at that time had turned down the offer. He felt but that the cranberries were still available.

a. Develop a model that can be utilized to maximize contribution (total sales less variable costs) with only the 3,000,000 pounds of cranberries.

b. Deliberate whether the additional 80,000 pounds of Grade a cranberries should be purchased. Describe your decision.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M921250

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