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the poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities.A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron.Formulate the linear programming model for this situation.

Sagot :

Answer:

- Min Z = $400C + $200A

Step-by-step explanation:

The linear programming model deals with the minimization or maximization of a linear function of several variables and inequalities. This method assists the industries in minimizing costs and maximizing production.

In the given situation,

The Linear programming model would be:

Min Z = $400C + $200 A

which is based on:  

150 mg of vitamin K in corn C + 250 mg of vitamin K in AlfaAlfa  ≥ 500

75 mg of iron in Corn + 50 mg of iron in AlfaAlfa ≥ 400

∵ C, A ≥ 0

Thus, the equation would be,

Min Z = $400C + $200 A

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