Final answer:
The Slavin Corporation must choose the most cost-effective production technology based on machine and labor costs to efficiently use machine hours and maximize profit, with the choice varying depending on the relative cost changes of labor and machines.
Step-by-step explanation:
The subject of the question concerns the efficient allocation of machine hours to maximize production and profit for Slavin Corporation, which manufactures two products that demand more capacity than is available on a single machine. This scenario necessitates examining different production technologies and their associated costs to determine which one yields the lowest total cost, thus improving profitability.
When considering production technology choices, Slavin Corporation should evaluate the total costs associated with each option, considering both labor and machine costs. If machine hours become cheaper, it is logical to choose a production method that leverages more machines and less labor, especially when faced with union demands for higher wages. As such, the choice of technology will depend on the relative costs of labor and capital.
In situations where machine costs increase, it might be more economical to shift towards a production technology that uses more labor, hence choosing production technology 2. On the other hand, if labor costs increase, adopting a production technology that utilizes more machines, like production technology 3, could be more beneficial. Each decision aims to minimize the total cost and maximize the company's production and profitability within the machine's capacity.