Billups's Food Grain Company manufactures two blends of animalfeed (Regular and Special diet) using a mixture of three grains: wheat, soybean, and corn. Regular feed blend sells for $25 per 50 pound bag, whereas Special Diet blend sells for $40 per 50 pound bag. The cost per pound of wheat, soybean, and corn, as well as the respective availability of each of these grains is shown below:
 Cost / PoundPounds Available
Wheat.1720,000
Soybean.09100,000
Corn.1350,000
   
The blended Regular feed grain product must be comprised of at least 15% wheat and at least 40% corn. The blended Special Diet feed grain product must be comprised of at least 35% wheat and at least 25% corn.


Develop a linear programming formulation that will determine the number of pounds of each blend to produce so as to maximize profit.
Decision Variables are:
Xr = #lbs Regular
Xs = #lbs Special
Objective Function is:
Xr = (25/50) - (.15*.17) - (.4*.13) - (.45*.09) = .5 - .0255 - .052 - .0405 = .382
Xs = (40/50) - (.35*.17) - (.25*.13) - (.4*.09) = .8 - .0595 - .0325 - .036 = .672
Maximize .382Xr + .672Xs
Constraints are:
.15Xr +.35Xs <= 20,000 for Wheat
.45Xr +.40Xs <= 100,000 for Soybean
.4Xr +.25Xs <= 50,000 for Corn