State the corresponding corner point (x, y) for the given simplex tableau.

Steps to Solve

1. Identify basic and non-basic variables

In a simplex tableau, the basic variables are those that have a column with a single '1' and the rest '0's. The non-basic variables are set to zero. From the given tableau, we can identify that $s_1$ and $y$ are basic variables. This implies that $x$ and $s_2$ are non-basic variables and thus equal to 0.

2. Write the equations corresponding to the basic variables

From the last row of the tableau, we can write the equation for $s_1$ as: $s_1 + 0x + 0y + 0s_2 + 0s_3 = 10 \implies s_1 = 10$. From the second to last row of the tableau, we can write the equation for $y$ as: $0s_1 + 0x + y + 0s_2 + \frac{1}{2}s_3 = 15 \implies y + \frac{1}{2}s_3 = 15$.

3. Solve for the basic variables by setting non-basic variables to zero

Since $x$ and $s_2$ are non-basic variables, we set them to zero. To find the values of the basic variables $s_1$ and $y$, we also need to determine the value of $s_3$. Here, all we need to determine is the values of $x$ and $y$.

Since $x$ is a non-basic variable, $x=0$. Now, we need to find $y$. We know that $y + \frac{1}{2}s_3 = 15$. We need to recognize here that since only $x$ and $s_2$ were stated as non-basic (not the other slack variable $s_3$), we cannot assume that $s_3 = 0$. The third equation (though not necessary to immediately solve for $x$ and $y$) is given by $s_3+0s_2+0x+30s_1=0$, so $s_3=0$. Therefore, $y + \frac{1}{2}(0) = 15$, which means $y = 15$.

4. State the corner point

The corner point is $(x, y) = (0, 15)$.