Explanation Given information: A recently installed machine earns the company revenue at a continuous rate of 60 , 000 t + 45 , 000 dollars per year during the first six months of the operation and at the continuous rate of 75 , 000 dollars per year after the six months. The cost of the machine is $150,000, interest rate is 7% per year, compounded continuously, and t is time in years since the machine was installed. Formula used: Present value , P = ∫ 0 M S ( t ) e − r t d t Where S ( t ) is sale rate per year, t is the time, and r is rate of interest. Calculation: A recently installed machine earns the company revenue at a continuous rate of 60 , 000 t + 45 , 000 dollars per year during the first six months of the operation. For 0 ≤ t ≤ 0.5 , S ( t ) = 60 , 000 t + 45 , 000 The continuous rate of 75 , 000 dollars per year after the six months. ⇒ For 0.5 ≤ t ≤ 1 , S ( t ) = 75 , 000 The interest rate is 7% per year compounded continuously. ⇒ r = 0.07 The present value of the revenue earned by the machine during the first year of operation is P = ∫ 0 1 S ( t ) e − ( 0 To determine (b) To find: The time taken for the machine to pay for itself.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 6.5, Problem 14P

To determine

(a)

To find:

The present value of the revenue earned by the machine during the first year of operation.

To determine

(b)

To find:

The time taken for the machine to pay for itself.

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Chapter 6.5, Problem 13P

Chapter 6.5, Problem 15P

Chapter 6 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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(a) To find: The present value of the revenue earned by the machine during the first year of operation.

Solution Summary: The author calculates the present value of the revenue earned by the machine during the first year of operation.