Use the simplex method to solve the linear programming problem.
$$\begin{array}{ll}\text{ Maximize }& z=4x_1+6x_2\\ \text{ subject to: }& x_1-5x_2\le 30\\ & 3x_1-4x_2\le 18\\ \text{ with }& x_1\ge 0,x_2\ge 0\end{array}$$
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answers.)
A. The maximum is $◻$ when $x_1=◻$ and $x_2=◻$.
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 ：$\boxed{{\displaystyle \text{The correct choice is B. There is no maximum.}}}$