The poultry farmer decided to make his own chicken scratch b

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.

Solution

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