Use the simplex method to solve the linear programming problem.
\[
\begin{array}{ll}
\text { Maximize } & z=4 x_{1}+6 x_{2} \\
\text { subject to: } & x_{1}-5 x_{2} \leq 30 \\
& 3 x_{1}-4 x_{2} \leq 18 \\
\text { with } & x_{1} \geq 0, x_{2} \geq 0
\end{array}
\]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answers.)
A. The maximum is $\square$ when $x_{1}=\square$ and $x_{2}=\square$.
B. There is no maximum.

Step 1 ：Convert the inequalities to equations by introducing slack variables.

Step 2 ：Set up the initial simplex tableau.

Step 3 ：Identify the pivot column (the column corresponding to the variable to increase) and the pivot row (the row corresponding to the variable to decrease).

Step 4 ：Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.

Step 5 ：Repeat steps 3 and 4 until an optimal solution is found.

Step 6 ：The optimization process indicates that the problem appears to be unbounded. This means that there is no maximum value for the objective function under the given constraints.

Step 7 ：\(\boxed{\text{The correct choice is B. There is no maximum.}}\)