Question: The Elixer Drug Company produces a drug from to ingredients. Each ingredient contains the same 3 antibiotics, in different proportions. 1 gram of ingredient 1 contributes 3 units, and 1 gram of ingredient 2 contributes 1 unit of antibiotics 1; the drug requires 6 units. At least 4 units antibiotics 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 ingredient 1 is $80, and the cost for a gram 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.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.