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Linear Programming: Drug Company Analysis

A 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 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
- Solve this model using a graphical analysis
- Determine any unused resources at the optimum point

Solution Preview

Please see the attached Word file for result. I have also attached a PowerPoint file for your reference.

a. Refer to the attached Word document.

b. Solve this model by using graphical analysis.

Draw all equations 1, 2, and 3, you will get the pink area as the feasible ...

Solution Summary

This solution provides a detailed, step by step response which clearly indicates how to solve this linear programming problem. A Word document is attached and contains the full solution, including all necessary calculations, equations and graphs. A PowerPoint document is also attached and acts as a reference guide for linear programming problems in general.