LP Examples Water allocation Resources Allocation Problem A

LP Examples Water allocation

Resources Allocation Problem • A farmer operates three farms. Each farm is managed by a different one of his sons. Limits on land, water, and water requirements are given in the table below. Three crops may be planted on each farm, but due to limitations on equipment availability, two of the crops are limited in total area that may be planted. Also, for equity among the sons, the fraction of each farmland that may be planted must be equal. The crop profit figures given in the table below are net after deleting estimated costs. The total water right for all farms is 106 m 3. • Develop an LP model for determining how much of each crop should be planted on each farm.

Resources Allocation Problem • The LP problem can be formulated as follows: • Define Xij as hectares (ha) planted on farm i to crop j. • The model structure will be: Max Profit (Total for 3 farms) s. t. : 1. Land planted <= available land (each farm) 2. Total of each crop <= equip limits (each crop) 3. Total water use <= total available 4. Fraction of area planted = fraction on other farms on each farm

Resources Allocation Problem Max Z = 0. 2 (XA 1 + XB 1 + XC 1) + 0. 4 (XA 2 + XB 2 + XC 2) + 0. 5 (XA 3 + XB 3 + XC 3) s. t. • XA 1 + XA 2 + XA 3 <= 40 • XB 1 + XB 2 + XB 3 <= 50 • XC 1 + XC 2 + XC 3 <= 70 • XA 2 + XB 2 + XC 2 <= 80 • XA 3 + XB 3 + XC 3 <= 50 • 0. 5 (XA 1 + XB 1 + XC 1) + 0. 7 (XA 2 + XB 2 + XC 2) • + 1. 0 (XA 3 + XB 3 + XC 3) <= 106 • XA 1 + XA 2 + XA 3 = XB 1 + XB 2 + XB 3 • XA 1 + XA 2 + XA 3 = XC 1 + XC 2 + XC 3