Final answer:
The student is asked to determine the optimum completion duration for an excavation task, taking into account manpower and equipment efficiency, and to calculate the minimum possible corresponding costs, factoring in direct expenses and potential penalties for delays.
Step-by-step explanation:
The question asks for the determination of the optimum possible completion duration and the calculation of its minimum possible corresponding costs in the context of an excavation project. The excavation firm is tasked to excavate and dispose of 48,000 m³ of soil in a stipulated time frame with financial penalties for delays.
We need to consider our available resources of labor and equipment to find the most time- and cost-efficient method for completing this task without incurring liquidated damages.
To calculate the optimum completion duration, we will assume that our workforce and equipment can optimally perform based on past performance averages, similar to the historical accounts of earthwork per man-day in medieval Egypt.
We need to ascertain the volume of soil that each combination of labor and equipment can move per day. Then we divide the total volume of soil, 48,000 m³, by the daily productivity rate to find the number of days required for completion.
The minimum possible corresponding costs will include direct costs like labor wages, equipment rental, and operation costs, as well as indirect costs such as the potential for liquidated damages if the project exceeds the 30 working days limit. By keeping the project within this time frame, the company avoids both the additional financial burden and the risk of not receiving future contracts due to excessive delays.