# Estimating Cost for Assembling Electronic Boxes

## What is the estimated cost to assemble all 10 units of electronic boxes?

Given data:

- First box assembly time: 220 hours
- Learning rate: 10%
- Hourly labor rate: $194

## Estimated Cost Calculation:

To estimate the cost of assembling all 10 electronic boxes, we can use the concept of the learning curve. The learning curve is a mathematical model that predicts how the time or cost required to complete a task decreases as workers become more experienced.

## Estimating Cost for Assembling Electronic Boxes

The learning curve is a useful tool for estimating the cost and time required to complete a project as workers gain experience. In this case, the learning rate is 10%, meaning that with each doubling of the cumulative production quantity, the time required decreases by 10%.

Given that the first box took 220 hours to assemble, we can calculate the time it would take to assemble each subsequent box using the learning curve formula:

## Time(n) = Time(1) * (n^log(0.9) / log(2))

For the first box, the time taken is 220 hours. Using the formula, we can calculate the time to assemble the second box, which is approximately 196.94 hours. Similarly, the time to assemble the third box is approximately 184.68 hours.

Instead of calculating the time for each individual box up to the tenth unit, we can use a simplified formula to find the total time to assemble all 10 units:

## Total Time = Time(1) * (1 - (1 - learning rate)^n) / learning rate

Plugging in the values, we get an estimated total time of approximately 970.65 hours. To find the total cost, we multiply this by the hourly labor rate:

## Cost = Total Time * Hourly Labor Rate

After calculating, the estimated cost to assemble all 10 electronic boxes is approximately $188,303. This estimation assumes the learning curve remains consistent for all units and does not include other project costs like materials or overhead expenses.