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74238555-Chapter-1-Examples-1

74238555-Chapter-1-Examples-1 - Example 1.6 The diet...

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Example 1.6 The diet problem Green Farm uses at least 800 kg of special feed daily. The special feed is a mixture of corn and soybean meal with the following composi- tions: kg per kg of feedstuff Feedstuff Protein Fiber Cost ($ per kg) Corn 0.09 0.02 0.30 Soybean 0.60 0.06 0.90 The dietary requirements of the total feed stipulate at least 30% protein and at most 5% fiber. Green Farm wishes to determine the daily minimum-cost feed mix. Formu- late the problem as an LP problem. 1
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Solution Decision variables : x 1 = Amount (kg) of corn in the daily mix x 2 = Amount (kg) of soybean in the daily mix Constraints : Daily amount requirement: x 1 + x 2 800 Dietary requirements: Protein: 0 . 09 x 1 + 0 . 60 x 2 0 . 3( x 1 + x 2 ) Fiber: 0 . 02 x 1 + 0 . 06 x 2 0 . 05( x 1 + x 2 ) Objective : minimize 0 . 3 x 1 + 0 . 9 x 2 2
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Thus, the complete model is minimize 0 . 3 x 1 + 0 . 9 x 2 subject to x 1 + x 2 800 - 0 . 21 x 1 + 0 . 3 x 2 0 - 0 . 03 x 1 + 0 . 01 x 2 0 x 1 ,x 2 0 3
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Example 1.8 Bank Loan Policy The ABC bank is in the process of formulat- ing a loan policy involving a total of $12 mil- lion. Being a full-service facility, the bank
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