Answer:
Explanation:
To determine the number of hours required to produce the 175th unit, we need to consider the concept of learning curves. The learning curve theory suggests that as workers gain experience and familiarity with a task, their productivity improves over time.
Typically, the learning curve is expressed as a percentage reduction in time or cost with each doubling of production units. A common learning curve used is the 80% learning curve, which means that each time the production doubles, the time required decreases by 20%.
Given that it took 240 hours of direct labor to produce the first unit, we can use the 80% learning curve to estimate the time required for the 175th unit.
First, we need to determine the number of doublings from the first unit to the 175th unit. We can calculate this using the formula:
Doublings = log2(N), where N is the unit number.
Doublings = log2(175) ≈ 7.459
Next, we apply the learning curve formula:
Time Required = Initial Time * (Learning Curve)^Doublings
Time Required = 240 * (0.8)^7.459
Time Required ≈ 50.82 hours
Therefore, it is estimated that it will take approximately 50.82 hours to produce the 175th unit, assuming an 80% learning curve is applicable.