Question: 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 1 gram of 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 gramof ingredient 1 contributes 1 is $80, and the cost for gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of gram of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.

1. Formulate a linear programming model for this problem.
   
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