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# Convert the LPP:add slack, surplus and Artificial variables

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Consider the following LP problem:

Maximize earnings = \$0.80X1 + \$0.40X2 + \$1.20X3 ? \$0.10X4
subject to: X1 + 2X2 + X3+ 5X4= 150
X2- 4X3 + 8X4 = 70
6X1 + 7X2 + 2X3 ? X4 = 120
X1,X2,X3,X4 = 0

(a) Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problem's objective function.
(b) Set up the complete initial simplex tableau for this problem. Do not attempt to solve.
(c) Give the values for all variables in this initial solution.

#### Solution Preview

9-19 Consider the following LP problem:
maximize earnings = \$0.80X1 + \$0.40X2 + \$1.20X3 — \$0.10X4
subject to: X1 + 2X2 + X3+ 5X4= 150
X2- 4X3 + 8X4 = 70
6X1 + 7X2 + 2X3 — X4 = 120
X1,X2,X3,X4 = 0
(a) Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problem's objective function.
(b) Set up the complete initial simplex tableau for this problem. Do ...

#### Solution Summary

Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problem's objective function.

\$2.19