Linear Programming The Table Method

Objectives and goals Solve linear programming problems using the Table Method

Example Solve the linear programming problem. Maximize subject to

Step 1 Change the inequalities to equations by adding slack variables, one for each equation. We will call the x and y in the initial inequalities, the initial variables. s t

Step 2 Create a table having the initial variables, slack variables, and the equation for P. xystP = 50x + 80y

Step 3 Place zeros strategically in each row. The number of zeros is the same as the number of initial variables. xystP = 50x + 80y

Step 4 For each row, substitute in zeros into the equations from step 1 and solve for the other variables. xystP = 50x + 80y

Step 4 (Continued) For each row, substitute in zeros into the equations from step 1 and solve for the other variables. xystP = 50x + 80y

Step 4 (Continued) For each row, substitute in zeros into the equations from step 1 and solve for the other variables. xystP = 50x + 80y

Step 4 (Continued) For each row, substitute in zeros into the equations from step 1 and solve for the other variables. xystP = 50x + 80y

Step 5 If both the initial and slack variables are not negative, then substitute in the values of the initial variables into the profit model P. xystP = 50x + 80y

Step 5 (continued) If both the initial and slack variables are not negative, then substitute in the values of the initial variables into the profit model P. xystP = 50x + 80y

Step 5 (continued) If both the initial and slack variables are not negative, then substitute in the values of the initial variables into the profit model P. xystP = 50x + 80y

Step 5 (continued) If both the initial and slack variables are not negative, then substitute in the values of the initial variables into the profit model P. xystP = 50x + 80y

Step 6 The highest value of P is the maximum and the values of the initial variables is when it happens xystP = 50x + 80y

The Idea Behind the Table Method Graph created using Desmos.com