Linear Programming - Operations
(Allocation Problem). A certain farming organization operates three farms of comparable productivity. The output of each farm is limited both by the usable acreage and by the amount of water available for irrigation. The data for the upcoming season are the following.
Farm Usable Acreage Water Available in Acre Feet
1 400 1,500
2 600 2,000
3 300 900
The organization is considering three crops for planting which differ primarily in their expected profit per acre and in their consumption of water. Furthermore, the total acreage that can be devoted to each of the crops is limited by the amount of appropriate harvesting equipment available.
Crop Maximum Acreage Water Consumption Acre Feet/Acre Expected Profit/ Acre
A 700 5 $400
B 800 4 $300
C 300 3 $100
In order to maintain a uniform workload among the farms, it is the policy of the organization that the percentage of the usable acreage planted must be the same at each farm. However, any combination of the crops may be grown at any of the farms. Formulate this as a linear programming problem.