Final answer:
In this case, the minimum cost plan for this company is to produce the required 1,040 engines over 8 months by utilizing overtime labor instead of hiring additional workers. This plan will result in a total cost of $792,500.
Step-by-step explanation:
To develop the minimum cost plan for the manufacturer of heavy truck engines, we can follow these steps:
1. Start with a level output/workforce plan: In a level plan, the company produces a constant number of engines each month, regardless of the demand. This plan helps to maintain stability in production and workforce.
2. Calculate the total demand over the planning horizon: Sum up the forecasted demand for each month. In this case, the total demand over 8 months is 1,040 engines.
3. Determine the required workforce: Divide the total demand by the production rate per worker to find the number of workers needed. In this case, the company produces 130 engines per month with 13 workers, so each worker produces 10 engines per month.
Therefore, the required workforce is 1,040 engines / 10 engines per worker per month = 104 workers.
4. Analyze the trade-off between hiring and overtime costs: Compare the cost of hiring additional workers with the cost of overtime labor. Calculate the difference between the regular labor cost ($500 per engine) and overtime labor cost ($750 per engine).
In this case, the difference is $750 - $500 = $250 per engine.
5. Compare the trade-off cost with the hiring cost: Calculate the cost of hiring additional workers by multiplying the hiring cost ($3,000 per worker) by the number of workers needed.
In this case, the cost of hiring additional workers is $3,000 per worker * (104 workers - 13 workers) = $273,000.
6. Calculate the cost of overtime labor: Multiply the number of engines produced through overtime by the overtime labor cost ($750 per engine). In this case, the number of engines produced through overtime is (130 engines per month * 13 workers) - 1,040 engines = 390 engines.
Therefore, the cost of overtime labor is 390 engines * $750 per engine = $292,500.
7. Compare the total cost of hiring and overtime: The total cost of the hiring plan is the sum of the hiring cost and the regular labor cost, while the total cost of the overtime plan is the sum of the overtime labor cost and the regular labor cost.
Compare these costs to determine the minimum cost plan.
In this case, the total cost of the hiring plan is $273,000 + ($500 per engine * 1,040 engines) = $823,000.
The total cost of the overtime plan is $292,500 + ($500 per engine * 1,040 engines) = $792,500.
Thus, the minimum cost plan is the overtime plan.
Therefore, the minimum cost plan for this company is to produce the required 1,040 engines over 8 months by utilizing overtime labor instead of hiring additional workers. This plan will result in a total cost of $792,500.