A farmer is preparing to plant a crop in the spring and needs to fertilize a filed.
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A farmer is preparing to plant a crop in the spring and needs to fertilize a filed. There are two brands of fertilizer to chose from, Super-gro and Crop-quick. Each brand yields a specific amount of nitrogen and phosphate, as follows Brand Chemical Contribution Nitrogen (lb/bag) phosphate (lb/bag) Super-gro 2 4 Crop-quick 4 3 The farmer’s field requires at least 16 pounds of nitrogen and 10 pounds of phosphate. Super-gro costs 6. The farmer wants to know how many bags of each brand to purchase in order to minimize the total cost of fertilizing. The formulated LP is: Let x1 = bags of Super-gro to buy Let x2 = bags of Crop-quick to buy Obj function : Min 12x1 + 6x2 subject to: 2x1 + 4x2 ≥ 16 4x1 + 3x2 ≥ 10 x1 ≥ 0 x2 ≥ 0 The sensitivity report is below: Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease 12 Super-gro 0 9 12 1E+30 9 13 Crop-quick 4 0 6 18 6 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease 8 Used Nitrogen 16 1.5 16 1E+30 2.666666667 8 Used Phospate 12 0 10 2 1E+30 What is the value of the objective function at the optimal value? That is, how much will the farmer spend if he buys the optimal mix of Super-gro and Crop-quick.
Related Book For
College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
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