Linear Programming…

Problem: Scott owns a manufacturing company that produces two models of entertainment centers. The Athens requires 4 feet of fancy molding and takes 4 hours to manufacture. The Barcelona needs 15 feet of molding and 3 hours to manufacture. In a given week, there are 120 hours of labor available and the company has 360 feet of molding to use for the entertainment centers. The company makes a profit of \$9 on the Athens and \$12 on the Barcelona. How many of each model should the company manufacture to maximize its profit? (Problem adopted from Mathematics All Around 3rd Edition, Thomas L. Pirnot; Pearson Addison Wesley)

Part 1: Concepts of Linear Programming

1) Provide a definition of a constraint.

2) State the constraints for the problem

3) Provide a definition of an objective function.

4) State the objective function for this problem.

5) Identify whether or not you need to find a maximum or a minimum in order to solve the problem.

Part 2: Solve the Problem

1) Neatly graph the system of linear inequalities found in Part 1, indicate the feasible region, and identify the corners/vertices of the feasible region.

2) How many of each model should the company manufacture to maximize its profit?

Part 3: Impact Question Provide an example, or examples, of how the concepts covered in this assignment could be applied in life or future career choices other than manufacturing. The answer should show sufficient thought, effort, and research.

Resources: http://www.purplemath.com/modules/linprog.htm http://www.ehow.com/how_7831282_do-linear-programming-models.html

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