The University of Iowa is experimenting with a blend of soil amendments to be used in an analysis of variance study of the response of tomatoes to various amounts of sunlight. To perform this study, all other elements must be controlled so that the only variable is the sunlight. The minimum requirements for calcium, phosphorous, and potassium are 125 pounds, 150 pounds, and 120 pounds respectively. The soil amendment mixture from Prairie Gold consist of 25% calcium, 25% phosphorous, 12.5% potassium, and 37.5% other ingredients. It costs $0.40 per ounce. The mixture from Grinell Grow is 20% calcium, 25% phosphorous, 25% potassium, and 30% other ingredients. It sells for $0.50 per ounce.
Formulate a linear programming model that will allow the University of Iowa to conduct this experiment using a minimum cost blend of the two soil amendment mixtures. State clearly the Objective Function and the Constraints ( if any)