# Optimization-net-profit -v2

Document Sample

```					              Sub: Statistics                                                                     Topic: Optimization

Question:

To develop the linear programming model that maximizes the net
profit.
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Roundtree Cannery is a medium-sized company which produces and 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
meet 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, and 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. According to this report, about 20% of the
crop will be Grade A quality and the remaining portion will be Grade B. Mr. Jackson asked Mr.
Owens about the estimated 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 indicated that they could sell all of the whole
canned cranberries they could produce, the expected demand for cranberry juice and jellied
cranberry was limited. He reminded the group that the selling prices had been set in light of
the long-term marketing strategy of the company and that the potential sales had been
forecasted at these prices.

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Sub: Statistics                                                                     Topic: Optimization
Exhibit 1

Demand Forecasts

Product                         Selling Price per Case           Demand Forecast (Cases)

24 packages/case whole cranberries                          \$4.00                          800,000

24 cans/case choice peach halves                          \$5.40                           10,000

24 cans/case peach nectar                             \$4.60                            5,000

24 bottles/case cranberry juice                          \$4.50                           50,000

24 can/case cooking apples                            \$4.90                           15,000

24 cans/case jelled cranberry sauce                        \$3.80                           80,000

Ms. Adams, after looking at the demand estimates, said that it appeared like the company
should do quite well on the cranberry crop this year. With the new accounting system that had
been set up, she had been able to compute 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 signed
contracts agreeing to purchase the grower=s production at an average delivered price of 6
cents per pound, Ms. Adams had computed the cranberry products= contributions shown in
Exhibit 2 (Product Item Profitability by Case). Exhibit 2 was distributed to the officers at the
meeting.

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Sub: Statistics                                                                     Topic: Optimization
Exhibit 2

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Description: To develop the linear programming model that maximizes the net profit.
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