A company is producing a new product. Due to the nature of the product, the time

Question

A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2 +0.6(1/x), where T(x) is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 5: units 15 through 20. The worker requires hours to produce units 1 through 5. (Round to two decimal places as needed.) The worker requires hours to produce units 15 through 20. (Round to two decimal places as needed.)

Explanation / Answer

time required for a new worker to produce units 1 through 5 is =[1 to 5]T(x) dx

time required for a new worker to produce units 1 through 5 is =[1 to 5](2+0.6(1/x)) dx

time required for a new worker to produce units 1 through 5 is =[1 to 5](2x +0.6ln(x))

time required for a new worker to produce units 1 through 5 is =(2*5 +0.6ln(5))-(2*1 +0.6ln(1))

time required for a new worker to produce units 1 through 5 is =(10 +0.6ln(5))-(2+0)

time required for a new worker to produce units 1 through 5 is =8.97 hours

time required for a new worker to produce units 15 through 20 is =[15 to 20]T(x) dx

time required for a new worker to produce units 15 through 20 is =[15 to 20](2+0.6(1/x)) dx

time required for a new worker to produce units 15 through 20 is =[15 to 20](2x +0.6ln(x))

time required for a new worker to produce units 15 through 20 is =(2*20 +0.6ln(20))-(2*15 +0.6ln(15))

time required for a new worker to produce units 15 through 20 is =10.17 hours

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