Solve the linear programming problem using the simplex method. \[ \begin{array}{lr} \text { Maximize } & P=25 x_{1}+100 x_{2} \\ \text { Subject to } & x_{1}+5 x_{2} \geq 25 \\ & x_{1}, x_{2} \geq 0 \end{array} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The optimal solution is $P=\square$ when $x_{1}=\square$ and $x_{2}=$ (Simplify your answers. Type integers or fractions.) B. There is no optimal solution.

Step 1 ：The problem is a linear programming problem and we are asked to solve it using the simplex method. The objective function is to maximize \(P = 25x_1 + 100x_2\) subject to the constraints \(x_1 + 5x_2 \geq 25\) and \(x_1, x_2 \geq 0\).

Step 2 ：The first step in the simplex method is to convert the inequalities into equalities by introducing slack variables. Then we will form the initial simplex tableau and perform row operations to find the optimal solution.

Step 3 ：The result indicates that the problem appears to be unbounded. This means that there is no optimal solution because the objective function can be increased indefinitely without violating any of the constraints.

Step 4 ：\(\boxed{\text{The correct choice is B. There is no optimal solution.}}\)