Cost Reduction Strategy: Boosting Efficiency with Lower Costs

How does reducing costs impact the optimal solution for a cabinetmaker?

Suppose cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? Explain.

Answer:

A reduction in the cost per hour for cabinetmaker 2 could potentially change the optimal solution towards using more hours from that cabinetmaker, leading to lower total costs. However, the exact impact depends on the specifics of the production function and other costs and constraints. Without further details, we cannot calculate the new objective function coefficients or the value of the new optimal solution.

The question relates to the changes in cost per hour for a cabinetmaker. If cabinetmaker 2 reduces its cost to $38 per hour, the new objective function coefficients for variables o2 and c2 would depend on the specifics of the function, including other costs and constraints. The effect on the optimal solution would also depend on these conditions.

However, based on the simple principle of cost minimization, a reduction in cost per hour for cabinetmaker 2 would mean that the optimal solution could potentially shift towards using more hours from that cabinetmaker, assuming quality and other factors remain constant. For instance, if we have a production function where o2 represents the hours worked by cabinetmaker 2 and c2 represents the cost per hour, a decrease in c2 (from, say, $40 to $38) would lower the total cost of production, possibly leading to higher profit or lower prices, depending on the company's strategy.

As for the value of the new optimal solution, without further specific information, we cannot calculate it.