LP Formulation Set 2.pdf - Common Business Applications of LP(Problem Set 2 1 Alexandra Bergson has subdivided her 2000 acre farm into 3 plots and has

LP Formulation Set 2.pdf - Common Business Applications of...

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Common Business Applications of LP (Problem Set 2) 1. Alexandra Bergson has subdivided her 2000 acre farm into 3 plots and has contracted with 3 local farm families to operate the plots. Plot 1 is 500 acres, plot 2 is 800 acres and plot 3 is 700 acres. The size of each plot has been determined by the capabilities of each local farmer. She has instructed each sharecropper to plant three crops: corn, peas and soybeans which yield profits of $600, $450 and $300 respectively. Farming policies restrict the maximum acreage of corn to 900 acres, peas to 700 acres and soybeans to 1000 acres. Any of the three crops may be planted on any of the plots; however Alexandra has placed the following restrictions on the farming operation. At least 60% of each plot must be under cultivation. To ensure that each sharecropper works according to his or her potential resources (which determined the acreage allotment), she wants the same proportion of each plot to be under cultivation. Her objective is to determine how much of each crop to plant on each plot to maximize profit. Formulate a linear programming model for this problem. 2. A ship has two cargo holds, one fore and one aft. The fore cargo hold has a weight capacity of 70,000 pounds and a volume capacity of 30,000 cubic feet. The aft hold has a weight capacity of 90,000 pounds and a volume capacity of 40,000 cubic feet. The ship-owner has contracted to carry loads of packaged beef and grain. The total weight of the available beef is 85,000 pounds and the total weight of the available grain is 100,000 pounds.
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  • Winter '12
  • LauraAlan

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