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The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics in different proportions.

The Elixer Drug Company produces a drug from two ingredients.  Each ingredient contains the same three antibiotics in different proportions.  One gram of ingredient 1 contributes 3 units, and ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units.  At least 4 units of antibiotic 2 are required, and the ingredients each contribute 1 unit per gram.  At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units.  The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50.  The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.
Formulate a linear programming model for this program.

The Elixer Drug Company produces a drug from two ingredients. Each
ingredient contains the same three antibiotics in different proportions.
One gram of ingredient 1 contributes 3 units, and ingredient 2
contributes 1 unit of antibiotic 1; the drug requires 6 units. At least
4 units of antibiotic 2 are required, and the ingredients each
contribute 1 unit per gram. At least 12 units of antibiotic 3 are
required; a gram of ingredient 1 contributes 2 units, and a gram of
ingredient 2 contributes 6 units. The cost for a gram of ingredient 1
is $80, and the cost for a gram of ingredient 2 is $50. The company
wants to formulate a linear programming model to determine the number of
grams of each ingredient that must go into the drug in order to meet the
antibiotic requirements at the minimum cost.
Formulate a linear programming model for this program.

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