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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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