Linear Programming Problem: Cabinetmaker 2 Cost Reduction Analysis
What effect would a cost reduction to $38 per hour have on the optimal solution for Cabinetmaker 2?
Would the optimal solution change with this cost reduction?
Effect of Cost Reduction on Optimal Solution
The cost reduction for Cabinetmaker 2 from $40 to $38 per hour, along with the adjustments to the objective function coefficients for producing o2 and c2, have no effect on the optimal solution. The optimal solution remains unchanged.
When Cabinetmaker 2 reduces its cost to $38 per hour, the optimal solution in the linear programming problem remains the same. This demonstrates the robustness and stability of the original solution.
The fundamental principles of linear programming and sensitivity analysis ensure that the optimal solution is determined based on the objective function coefficients and constraints. In this case, even though the cost per hour for Cabinetmaker 2 has changed, the optimal solution value of $3,552.50 remains unaffected.
Key factors contributing to the unchanged optimal solution include:
1. Objective Function Coefficients:The adjustments to the coefficients for products o2 and c2 do not alter the relative profitability of these products compared to o1 and c1. The balance of contributions to the total objective value remains consistent.
2. Optimality Conditions:The optimality conditions in linear programming ensure that the optimal solution maximizes or minimizes the objective value. The original solution satisfies these conditions, and the new coefficients do not disrupt this balance.
3. Sensitivity Analysis:By analyzing the impact of changes in costs and coefficients, it is evident that the optimal solution for Cabinetmaker 2 is resilient to these adjustments. The solution remains optimal and retains its value.