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Optimizing Farming Income with Cattle and Trees

Determine the best mix of cattle and tree farming to maximize income on your 1200-acre land. Explore constraints, ranging analysis, and LP problem structure for informed decision-making.

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Optimizing Farming Income with Cattle and Trees

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  1. Assume you own you own 1200 acres of land, and have $142,500 to invest. Your land is most suited for tree farming or raising cattle. You want to decide what is the best mix of trees and cattle to maximize your income. Cattle require 1 acre per animal, and cost $75 Trees require 1 acre per 500, and cost $300 per lot of 1000 Annual returns are $9/steer, and $10 per acre of trees

  2. Constraints and Ranging Analysis Land Constraint Capital Constraint Optimum – 500 cattle 350 lots of trees

  3. “Zoom in” near optimum to see Results of Ranging Analysis better Z=9X1 + 20X2 500 steer, 350 lots of trees =$11,500

  4. “Zoom in” near optimum to see Results of Ranging Analysis better Z=9X1 + 20X2 500 steer, 350 lots of trees =$11,500 Z=5X1 + 20X2 500 steer, 350 lots of trees=$9,500

  5. Changes in “Technological Coefficients” And Shadow Prices New land Constrain add 100 acres Capital constraint Old land constraint Z=9X1 + 20X2 500 steer, 350 lots of trees =$11,500 Z=9X1 + 20X2 700 steer, 300 lots of trees =$12,300 $800 gain by adding 100 acres

  6. Formal Structure of LP problem Maximize Z = C1X1 + C2X2 + C3X3… Such that, A11X1 + A12X2 + A13X3 … <=B1 A21X1 + A22X2 + A23X3 … <=B2 A31X1 + A32X2 + A33X3 … <=B3 A41X1 + A42X2 + A43X3 … <=B4 X1>=0 X2>=0 … Ci = Objective function coefficients (cost coefficients) Aij = Technological coefficients Bi = Right hand side constraints

  7. Integer Programming

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