1. The simplex method is used to solve linear programming problems of the form: maximize or minimize a linear objective function subject to linear equality and inequality constraints. 2. Suppose the problem is to maximize $Z = c_1x_1 + c_2x_2 + \dots + c_nx_n$ subject to constraints $Ax \leq b$, where $x \geq 0$. 3. The first step is to convert inequalities into equalities by adding slack variables to the constraints. 4. Write the initial simplex tableau including the coefficients of variables, slack variables, and the constants from the constraints. 5. Identify the pivot column by choosing the most negative coefficient in the objective function row. 6. Identify the pivot row by dividing the rightmost column values by the corresponding positive entries in the pivot column, choosing the smallest non-negative ratio. 7. Perform pivot operations to make the pivot element 1 and all other elements in the pivot column 0. 8. Repeat steps 5-7 until there are no negative coefficients in the objective function row, meaning the optimal solution is reached. 9. The solution values of variables and the maximum value of $Z$ are read from the final tableau. If you provide the specific problem with objective function and constraints, I can demonstrate these steps explicitly for that problem.