The image provided shows a tableau, likely from a linear programming or simplex method problem. To find $x$, $y$, and $z$ (the basic variables), we'll use the fact that these are generally assigned based on which variables correspond to unit columns (columns with exactly one "1" and all other entries in the column are "0"). Here's how we analyze this:

• $x$ column: It contains a "1" in the row labeled "t" and "0" everywhere else. So, $x = 242$, which is the right-hand side (RHS) value in row "t".

• $y$ column: It contains a "1" in the row labeled "s" and "0" everywhere else. So, $y = 58$, the RHS value in row "s".

• $z$ column: There is no unit column for $z$. This means that $z$ is a non-basic variable, which typically means that $z = 0$.

Thus, the values are:

• $x = 242$
• $y = 58$
• $z = 0$

Would you like a detailed explanation of how this tableau analysis works or have any questions?

Additional Questions:

1. What is the role of basic and non-basic variables in a simplex tableau?
2. How do we interpret the final row of this tableau in the context of an objective function?
3. Can you explain how slack or surplus variables fit into this tableau?
4. How would you solve a maximization problem using this tableau?
5. What happens if one of the variables in the tableau is negative on the RHS?

Tip:

When analyzing a simplex tableau, always start by identifying which columns represent basic variables, as their corresponding values can be easily read from the RHS of their respective rows.