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; the drug requires 6 units. at l east 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each 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 problem
(Showing the procedure, and use QM if needed)