Question: Explicitly state the following:

1. Decision Variables: Express the decision variable in mathematical notation, and state what each decision variable stands for in words.
2. Constraints: Write each constraint in mathematical notation, and state what it stands for in words.
3. Objective function: Write the objective in mathematical notation, and state what it stands for in words.
4. Following steps (1) – (3), write the entire model as a linear programming (LP) formulation.
5. Solve the LP using GAMS, and determine the optimal values of: decision variables, objective function, and constraints.

A steel manufacturer produces four sizes of I-beams: small, medium, large, and extra large. These beams can be produced on any one of the three machine types: A, B, C. The length in feet of the I-beams that can be produced on the machines per hour is summarized.

Assume that each machine can be used up to 50 hours/week, and that the hourly operating costs of these machines are $30, $50, and $80, respectively. Further suppose that 10000, 8000, 6000, and 6000 feet of the different size I-beams are respectively required weekly. Formulate this machine scheduling problem as a linear program to minimize operating costs.

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document