The poultry farmer decided to make his own chicken scratch by combining alfalfa

Question

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 thos 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.

Explanation / Answer

The objective would be to minimize cost ot make his own chicken scratch , so we need to find optimal quantity of corn and alfalfa while providing required nutrients

Objective function:

Min : 400 * x + 200 * y

where x = number of rail cars of corn

y = number of rail cars of alfalfa

constraints:

the minimum requirement of vitamin k is 500 milli grams

so ,

x * 150 + y * 250 >= 500

the mimunum requirement of iron is 400 milligrams

so,

x * 75 + y * 50 >= 400

x,y >=0

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