State the corresponding corner point (x, y) for the given simplex tableau. The tableau is provided, identify the values of x and y.
Understand the Problem
The question requires interpreting a simplex tableau to determine the corresponding corner point (x, y) of a linear programming problem. The tableau provides the values of the variables at a specific corner point. We need to identify the basic variables and their corresponding values to extract the (x, y) coordinates.
Answer
$(x, y) = (5, 0)$
Answer for screen readers
$(x, y) = (5, 0)$
Steps to Solve
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Identify the basic variables: In a simplex tableau, the basic variables are those that have a column with a single '1' and the rest '0's. These columns are called unit columns.
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Determine the values of the basic variables: The value of each basic variable is found in the rightmost column (solution column) of the tableau, in the same row as the '1' in its unit column.
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Identify the non-basic variables: The non-basic variables are those that do not have a unit column. Their value is zero at the corner point represented by the tableau.
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Extract the x and y values: Based on the tableau, identify the rows that correspond to x and y. The values in the rightmost column for these rows are the values of x and y, respectively.
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Write the coordinates: Write the coordinates as an ordered pair (x, y).
$(x, y) = (5, 0)$
More Information
The corner point $(5, 0)$ represents a vertex of the feasible region for the linear programming problem. This is the point where the objective function is being evaluated in the simplex method to find the optimal solution.
Tips
A common mistake is to confuse the rows and columns when reading the values from the tableau. Another mistake is to incorrectly identify the basic and non-basic variables. Always look for the unit columns to correctly identify the basic variables and their corresponding values. Sometimes, students may try to perform calculations when the answer is directly available from the tableau.
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