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A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for one horsepower-hour will be $0.055 divided by the horsepower rating. 9,000 horsepower hours will be needed per year. a. Determine what horsepower should be specified for a minimum total annual cost. b. How do you know that you have minimized total cost per year? ... . a. To minimize total annual cost, the horsepower for the motor should be 29 horsepower. (Round to the nearest whole number.) b. Choose the correct answer below. O A. The answer to Part (a) minimizes total annual cost because the second derivative is less than zero for X>0. O B. The answer to Part (a) maximizes total annual cost because the second derivative is greater than zero for X> 0. O C. The answer to Part (a) minimizes total annual cost because the second derivative is greater than zero for X> 0. O D. The answer to Part (a) minimizes total annual cost because the first derivative is less than zero for X> 0.

A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for one horsepower-hour will be $0.055 divided by the horsepower rating. 9,000 horsepower hours will be needed per year. a. Determine what horsepower should be specified for a minimum total annual cost. b. How do you know that you have minimized total cost per year? ... . a. To minimize total annual cost, the horsepower for the motor should be 29 horsepower. (Round to the nearest whole number.) b. Choose the correct answer below. O A. The answer to Part (a) minimizes total annual cost because the second derivative is less than zero for X>0. O B. The answer to Part (a) maximizes total annual cost because the second derivative is greater than zero for X> 0. O C. The answer to Part (a) minimizes total annual cost because the second derivative is greater than zero for X> 0. O D. The answer to Part (a) minimizes total annual cost because the first derivative is less than zero for X> 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for one horsepower-hour will be $0.055 divided by the horsepower rating. 9,000 horsepower hours will be needed per year. a. Determine what horsepower should be specified for a minimum total annual cost. b. How do you know that you have minimized total cost per year? a. To minimize total annual cost, the horsepower for the motor should be 29 horsepower. (Round to the nearest whole number.) b. Choose the correct answer below. O A. The answer to Part (a) minimizes total annual cost because the second derivative is less than zero for X>0. O B. The answer to Part (a) maximizes total annual cost because the second derivative is greater than zero for X> 0. O C. The answer to Part (a) minimizes total annual cost because the second derivative is greater than zero for X> 0. O D. The answer to Part (a) minimizes total annual cost because the first derivative is less than zero for X>0.
Transcribed Image Text:A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for one horsepower-hour will be $0.055 divided by the horsepower rating. 9,000 horsepower hours will be needed per year. a. Determine what horsepower should be specified for a minimum total annual cost. b. How do you know that you have minimized total cost per year? a. To minimize total annual cost, the horsepower for the motor should be 29 horsepower. (Round to the nearest whole number.) b. Choose the correct answer below. O A. The answer to Part (a) minimizes total annual cost because the second derivative is less than zero for X>0. O B. The answer to Part (a) maximizes total annual cost because the second derivative is greater than zero for X> 0. O C. The answer to Part (a) minimizes total annual cost because the second derivative is greater than zero for X> 0. O D. The answer to Part (a) minimizes total annual cost because the first derivative is less than zero for X>0.
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