How many redundant constraints are shown in this diagram?

Practical Management Science
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Chapter2: Introduction To Spreadsheet Modeling
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**Linear Programming Diagram Explanation**

The diagram provided represents a linear programming problem, showing constraints and solutions for maximizing or minimizing a function. Here's a breakdown of the diagram elements:

**Axes:**
- The horizontal axis is labeled \( P \) and ranges from 0 to 1000.
- The vertical axis is labeled \( S \) and ranges from 0 to 1000.

**Points and Lines:**
- Three key points are marked:
  - \((0, 625)\)
  - \((100, 500)\) - labeled as the "optimal solution" with a profit of $59,300.
  - \((500, 0)\)
- A constraint is shown by the equation: \( 103.75 P + 97.85 S = 24,000 \).
- Another constraint line, which appears dashed and does not reach the optimal point, is shown but not labeled with an equation.

**Shaded Region:**
- The shaded area represents the feasible region where all the given constraints are satisfied.
- The optimal solution \((100, 500)\) lies within this region.

**Question:**
- "How many redundant constraints are shown in this diagram?"
  - Options are 0, 1, 2, and 3. 

The redundant constraint is one that does not affect the feasible region or the optimal solution, likely represented by the dashed line that doesn't reach the optimal point. This implies that there is at least one redundant constraint.

The diagram is a typical representation of a linear programming problem, illustrating how constraints influence the feasible region and identifying the optimal solution for maximizing or minimizing a given objective function.
Transcribed Image Text:**Linear Programming Diagram Explanation** The diagram provided represents a linear programming problem, showing constraints and solutions for maximizing or minimizing a function. Here's a breakdown of the diagram elements: **Axes:** - The horizontal axis is labeled \( P \) and ranges from 0 to 1000. - The vertical axis is labeled \( S \) and ranges from 0 to 1000. **Points and Lines:** - Three key points are marked: - \((0, 625)\) - \((100, 500)\) - labeled as the "optimal solution" with a profit of $59,300. - \((500, 0)\) - A constraint is shown by the equation: \( 103.75 P + 97.85 S = 24,000 \). - Another constraint line, which appears dashed and does not reach the optimal point, is shown but not labeled with an equation. **Shaded Region:** - The shaded area represents the feasible region where all the given constraints are satisfied. - The optimal solution \((100, 500)\) lies within this region. **Question:** - "How many redundant constraints are shown in this diagram?" - Options are 0, 1, 2, and 3. The redundant constraint is one that does not affect the feasible region or the optimal solution, likely represented by the dashed line that doesn't reach the optimal point. This implies that there is at least one redundant constraint. The diagram is a typical representation of a linear programming problem, illustrating how constraints influence the feasible region and identifying the optimal solution for maximizing or minimizing a given objective function.
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