Alexandra Bergson has subdivided her 2,000-acre farm into three plots and has contracted with three local farm families to operate the plots. She has instructed each sharecropper to plant three crops: corn, peas, and soybeans. The size of each plot has been determined by the capabilities of each local farmer. Plot sizes, crop restrictions, and profit per acre are given in the following tables: Plot Acreage 1 500 2 800 3 700 Maximum Acreage Profit/Acre Corn 900 $600 Peas 700 450 Soybeans 1,000 300 Any of the three crops may be planted on any of the plots; however, Alexandra has placed several restrictions on the farming operation. At least 60% of each plot must be under cultivation. Further, to ensure that each sharecropper works according to his or her potential and resources (which determined the acreage allocation), 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. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.
Alexandra Bergson has subdivided her 2,000-acre farm into three plots and has contracted with three local farm families to operate the plots. She has instructed each sharecropper to plant three crops: corn, peas, and soybeans. The size of each plot has been determined by the capabilities of each local farmer. Plot sizes, crop restrictions, and profit per acre are given in the following tables:
Plot Acreage
1 500
2 800
3 700
Maximum Acreage Profit/Acre
Corn 900 $600
Peas 700 450
Soybeans 1,000 300
Any of the three crops may be planted on any of the plots; however, Alexandra has placed several restrictions on the farming operation. At least 60% of each plot must be under cultivation. Further, to ensure that each sharecropper works according to his or her potential and resources (which determined the acreage allocation), 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.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
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