I am taking an online finite math class, so I don't have an instuctor to sit down with me and help me. The text book is so hard to follow. One of the problems I have having a hard time with gives an initial tableau and asks us to use the simplex method to solve each maximization linear programing problem with the given initial tableau.
I would just like to know the steps I take to solve this.
Thanks.
To solve a linear programming problem using the simplex method, you typically follow these steps:
Step 1: Formulate the problem
1. Write the objective function as a linear expression.
2. Write the constraints as linear inequalities or equalities. Make sure to include non-negativity constraints for all variables.
Step 2: Convert to a standard form
1. If your problem is a minimization problem, multiply the objective function by -1 to convert it into a maximization problem.
2. Transform any inequalities into equalities by adding slack, surplus, or artificial variables as needed.
3. Express any variable bounds as additional constraints.
Step 3: Create the initial tableau
1. Write all the variables, the objective function, and the constraints in a tabular form, using the standard form.
2. Identify the pivot column by selecting the most negative coefficient in the objective function row.
3. Identify the pivot row by selecting the smallest positive ratio of the right-hand side value to the corresponding element in the pivot column.
Step 4: Perform the pivot operation
1. Divide the pivot row by the pivot element to make the pivot element equal to 1.
2. Replace the other values in the pivot column with zeros by subtracting multiples of the pivot row from the other rows.
3. Update the tableau by performing the necessary calculations to find the new objective function coefficients and the new values of the variables.
Step 5: Check for optimality
1. If all coefficients in the objective function row are non-negative, the solution is optimal.
2. If there are still negative coefficients, repeat steps 3 and 4 until the solution becomes optimal.
Step 6: Obtain the solution
1. The values of the variables in the rightmost column give the optimal solution to the linear programming problem.
2. The objective function value at the bottom of the tableau represents the maximum value (in a maximization problem) or the minimum value (in a minimization problem) obtained at the optimal solution.
It's important to note that these steps are a general outline, and your specific problem may have additional complexities or variations. It's always a good idea to consult your textbook or additional resources for more detailed examples and explanations specific to your course material.