What is the objective function value for the first optimal solution of the three-variable LP?

What is the objective function value for the first optimal solution of the three-variable LP?

• A. 223.3333
• B. 228.0000
• C. 230.0000
• D. 250.0000

Answer: (B)

Optimal values for a linear program occur at corner points of the feasible region, and the first optimal solution is the first corner where you can no longer improve the objective by moving along an edge. Once you have the variable values at that corner, you evaluate the objective function there. In this case, those coordinates yield an objective value of 228.0000, so that is the correct value. The other numbers would come from evaluating the objective at other corners or at points that aren’t optimal yet, so they don’t represent the first optimal value.

Optimal values for a linear program occur at corner points of the feasible region, and the first optimal solution is the first corner where you can no longer improve the objective by moving along an edge. Once you have the variable values at that corner, you evaluate the objective function there. In this case, those coordinates yield an objective value of 228.0000, so that is the correct value. The other numbers would come from evaluating the objective at other corners or at points that aren’t optimal yet, so they don’t represent the first optimal value.