Chooko is a high-end dog food manufacturer. The company is in the process of designing a new, cheaper product made of beef and grain. You were asked to help with optimizing the beef and grain content of the new product, which will be sold in 1-pound (1 lb) bags.
Each pound of beef costs $1.50 while the unit cost for grain is only $0.80/lb. Each 1-pound bag of the dog food is required to contain at least 7.5 grams of Vitamin A and at least 8 grams of Vitamin B1. Each pound of beef contains 10 grams of Vitamin A and 6 grams of Vitamin B1, whereas each pound of grain contains 6 grams of Vitamin A and 12 grams of Vitamin B1. Chooko would like the new product to cost as little as possible while meeting the stated vitamin requirements.
Build a linear programming model and solve it. Describe your model building effort in your own words along the way and interpret the solution you obtain in the end.