Question

Zion Hospital has received initial certification from transplants . The hospital , however patients with the hospital picking the expenses . The cost per hour of surgery is estimated to be $ 5,200 . The very first transplant , just completed , required 32 hours . On the basis of research at the hospital , Beth Zion estimates that it will have an 75 % learning curve . Using Table E.3 , estimate the time it will take to complete : a ) the 10th transplant hours ( round your response to two decimal places ) .

Answer 1

Answer and explaination:
To estimate the time it will take to complete the 10th transplant, we can use the concept of the learning curve. The learning curve suggests that as more units are produced or procedures are performed, the time required decreases due to increased efficiency and experience gained.

According to the problem, the hospital has an estimated learning curve of 75%. This means that each time the number of transplants doubles, the time required to complete each subsequent transplant decreases by 25%.

To calculate the time for the 10th transplant, we'll use Table E.3, which provides the cumulative average time per unit for different learning curve percentages.

Let's find the cumulative average time per unit for a 75% learning curve:

Cumulative average time for the first unit = 100% of the time required = 32 hours (given)

Cumulative average time for the second unit = 75% of the time required = 0.75 * 32 hours

Cumulative average time for the fourth unit = 75% of the time required for the second unit = 0.75 * (0.75 * 32 hours)

Cumulative average time for the eighth unit = 75% of the time required for the fourth unit = 0.75 * (0.75 * (0.75 * 32 hours))

Now, let's find the cumulative average time for the 10th unit:

Cumulative average time for the 10th unit = 75% of the time required for the eighth unit = 0.75 * (0.75 * (0.75 * 32 hours))

To calculate the value, we'll round our response to two decimal places:

Cumulative average time for the 10th unit ≈ 0.75 * (0.75 * (0.75 * 32 hours))

Cumulative average time for the 10th unit ≈ 0.75 * (0.75 * (0.75 * 32))

Cumulative average time for the 10th unit ≈ 0.75 * (0.75 * 24)

Cumulative average time for the 10th unit ≈ 0.75 * 18

Cumulative average time for the 10th unit ≈ 13.5 hours

Therefore, it is estimated that the 10th transplant will take approximately 13.5 hours to complete.