M11 The Cullowhee Pharmaceutical Company produces a new experimental drug from two ingredients, Alpha and Beta. Each ingredient contains the same three antibiotics, X, Y, and Z in different proportions. One gram of ingredient Alpha contributes 4 units of antibiotic g and 1 gram of ingredient Beta contributes 2 units of antibiotic X. The final drug needs at least 7 units of antibiotic X. At least 8 units of antibiotic Y are required, and ingredient Alpha contributes 2 units each per gram and ingredient Beta contributes 3 units each per gram of ingredient. At least 14 units of antibiotic Z are required; a gram of ingredient Alpha contributes 3 unitsand a gram of ingredient Beta contributes 7 units. The cost for a gram of ingredient Alpha is $62 and the cost for a gram of ingredient Beta is $39. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug to meet the antibiotic requirements at the minimum cost. SOLUTION: The optimal solution, the value of the minimum cost should be $126.50. This problem should be used using the LP Graphing website. 1. a) Formulate this problem by defining decision variables, objective function, and constraints in standard format as specified/demonstrated in videos. 2. b) How many grams of ingredients Alpha and Beta should be included in the experimental drug (based on the optimal solution)? 3. c) Is putting 2 grams of Alpha and 1 gram of Beta in the drug feasible (not asking if it is optimal). Does it fall in the feasible region? Explain. 4. d) Is putting 1 gram of Alpha and 3 grams of Beta in the drug feasible (not asking if it is optimal). Does it fall in the feasible region? Explain. I 5. e) Insert a screen capture of your solution (showing the two "boxes\" showing formulation and plot as demonstrated in Module 7 Sample Problem #1) from LP Graphing website