Lets do some reverse engineering.

In the first part of this question, you will write a problem statement for a given LP model. In the second part, you will be challenged and surprised by yourself! You will formulate an LP model, using your own problem statement.

Hint:

• No restrictions on your problem statement topic/content.
• Use your imagination and be creative.
• You can get inspirations from Chapter 4 problems.

1. (5 points) Please do write a problem statement for the given linear programming model. In your problem statement, provide detailed descriptions for the decision variables.

Minimize 300 X₁ + 200 X₂ + 250 X₃

Subject to

4 X₁ + X₂ + 3 X₃ 6

9 X₁ + X₂ + 4 X₃ 10

10 X₁ + 40 X₂ + 3 X₃ 20

X₁,X₂, X₃ 0

Your answer should follow the template given below:

Problem statement: _{____________________________________________________________________________}

_{_____________________________________________________________________________________________________}

_{_____________________________________________________________________________________________________}

_{_____________________________________________________________________________________________________}

_{_____________________________________________________________________________________________________}

Description of decision variables:

X₁: _{__________________________________________________________________________________________________}

X₂: _{__________________________________________________________________________________________________}

X₃: _{__________________________________________________________________________________________________}

2. (5 points) Formulate a linear programming model using the Problem statement and Description of decision variables given in Part A.

To get full credit from part B, you need to provide the full model formulation, including:

• List of decision variables and their descriptions
• Objective function formulation

Complete list of constraint formulations, both operational constraints and constraints on decision variables