Final answer:
To develop an aggregate production plan, factors such as ending inventory targets, maximum overtime capacity, cost of labor, and economies of scale need to be considered. This requires balancing labor costs with machinery operations, taking into account the incentive to invest in better physical capital equipment to improve productivity within the constraints of overtime and machinery limits.
Step-by-step explanation:
The question is asking to develop an aggregate production plan considering the use of overtime to compensate for a product shortage, with an ending inventory target of 1,000 units by the end of the sixth month. With the maximum overtime capped at 400 units per month and wages at $24 an hour, it becomes necessary to balance the costs of labor against the cost of machine operation and capacity. This scenario is influenced by concepts such as economies of scale which dictate that as production increases, the average cost per unit decreases until a certain point, beyond which it remains constant or might even increase.
Given the wage increase, management could prefer investing in additional machinery which would allow current workers to produce more with better physical capital equipment, thus increasing productivity per worker and potentially reducing the need to hire additional staff. The detailed plan that needs to be developed would require a calculation of production quantities considering regular production hours, overtime hours, cost of labor, machine costs, and the constraints posed by the machinery and overtime limitations.