Question

. 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, 12½% potassium, and 37½% 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.

                     

Answer 1

Let x1 be the pounds of praire gold and x2 be the pounds of grinell grow used in the mixture

Objective function : Minimize Z = 6.4x1 + 8.0x2                   // minimize total cost

Subject to the following constraints :

0.25x1 + 0.25x2 >= 150         // constrain on the amount of phosporus in the mix

0.25x1 + 0.20x2 >= 125         // constrain on the amount of calcium in the mix

.125x1 + 0.25x2 >= 120        // constrain on the amount of potassium in the mix

x1>=0   // non negativity constraint on the amount of praire gold used

x2>=0   // non negativity constraint on the amount of grinell grow used

Since this is just upto formulation, we can end here.

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