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
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![5. An oil company is planning to extract oil from one of its fields, starting today at 1 = 0, where i is
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(1) = 10r²-³ 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(t) dr z ff(t) 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 a pnf (r) dr and op()g(t) dr
respectively. Compute these integrals. Which of the two extraction profiles earns the higher
revenue?
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2a6d1a3-4214-4aa6-95f9-7e82ded02ebc%2F8c962d96-d43a-4f2b-b94a-17ade058563d%2F1lg5xwq_processed.png&w=3840&q=75)
Transcribed Image Text:5. An oil company is planning to extract oil from one of its fields, starting today at 1 = 0, where i is
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(1) = 10r²-³ 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(t) dr z ff(t) 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 a pnf (r) dr and op()g(t) dr
respectively. Compute these integrals. Which of the two extraction profiles earns the higher
revenue?
1
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