State the corresponding corner point (x, y) for the given simplex tableau.
Understand the Problem
The question asks to find the corresponding corner point (x, y) from a given simplex tableau. In a simplex tableau, the basic variables are those with a column containing a single 1 and the rest 0s. The non-basic variables are set to 0, and you solve for the basic variables to find the corner point.
Answer
(0, 0)
Answer for screen readers
(0, 0)
Steps to Solve
- Identify the basic variables
The basic variables are those with a column containing a single 1 and the rest 0s. From the tableau, we see that $s_1$, $s_2$, $s_3$, and $P$ are basic variables.
- Set the non-basic variables to zero
Since $x$ and $y$ are not basic variables, we set them to 0: $x = 0$ and $y = 0$.
- Determine the corner point
The corner point is given by the values of $x$ and $y$. Thus, the corner point is $(0, 0)$.
(0, 0)
More Information
The corner point represents a vertex of the feasible region. In this simplex tableau, the non-basic variables, $x$ and $y$, are zero. Hence, the corresponding corner point is at the origin (0, 0).
Tips
Students might try to solve for x and y using the equations in the tableau, but that assumes the correct variables have been chosen to be basic. In this case the question asks only for the corner point represented by the current tableau.
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