5. An oil company is planning to extract oil from one of its fields, starting today at 1 = 0, where ris time measured in years. It has a choice between two different extraction profiles f and g giving the rates of output flow, measured in barrels of oil per year. Both extraction profiles last for 10 years, with f(t) = 10²-²³ and g(t) = ³ - 201²+100r for r in [0, 10]. (a) Sketch the two profiles in the same coordinate system. (b) Show that g(r) dr z f(r) dr for all in [0, 10]. (c) The company sells its oil at a price per unit given by p(t)=1+1/(t+1). Total revenues from the two profiles are then given by o pinf(n) dr and op(n)g(n) dr respectively. Compute these integrals. Which of the two extraction profiles earns the higher revenue?
5. An oil company is planning to extract oil from one of its fields, starting today at 1 = 0, where ris time measured in years. It has a choice between two different extraction profiles f and g giving the rates of output flow, measured in barrels of oil per year. Both extraction profiles last for 10 years, with f(t) = 10²-²³ and g(t) = ³ - 201²+100r for r in [0, 10]. (a) Sketch the two profiles in the same coordinate system. (b) Show that g(r) dr z f(r) dr for all in [0, 10]. (c) The company sells its oil at a price per unit given by p(t)=1+1/(t+1). Total revenues from the two profiles are then given by o pinf(n) dr and op(n)g(n) dr respectively. Compute these integrals. Which of the two extraction profiles earns the higher revenue?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,