Question

Suad​ Alwan, the purchasing agent for Dubai​ Airlines, has determined that the second plane took 18,000 hours to produce. Using an ​75% learning curve and a $30​-per-hour labor​ charge, he wants to determine the cost of the four additional planes. Time required for the fourth unit​ = ___ hours?

Answer 1

The time required for the fourth unit to be produced is 1,125 hours.

Step-by-step explanation:

The learning curve is a concept used in business and production analysis. It states that the time required to complete a task or produce an item decreases as the cumulative production doubles. In this case, the learning curve is 75%, which means that each time the cumulative production doubles, the time required decreases by 25%.

Given that the second plane took 18,000 hours to produce, we can use the learning curve to calculate the time required for the fourth unit. We start by finding the learning curve percentage using the formula: learning curve percentage = 100% - learning curve rate. In this case, the learning curve percentage is 100% - 75% = 25%.

Now, let's calculate the time required for the fourth unit. We use the formula: time required for the fourth unit = time required for the second unit * (learning curve percentage/100)^2. Since the second unit took 18,000 hours, the formula becomes: time required for the fourth unit = 18,000 * (25/100)^2 = 18,000 * (0.25)^2 = 18,000 * 0.0625 = 1,125 hours.

Therefore, the time required for the fourth unit is 1,125 hours.