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Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate d = 0.05. Hence this person's goal is to maximize ofs40 e-0.05tu(c(t))dt = of40e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H=e-0.05t(c(t))0.5+ (− c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a

Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate d = 0.05. Hence this person's goal is to maximize ofs40 e-0.05tu(c(t))dt = of40e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H=e-0.05t(c(t))0.5+ (− c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 1EA: Suppose that a particular plot of land can sustain 500 deer and that the population of this...
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Please see the attached problem. How do you find the continuous rate in percent per year of a person's wine consumption decreasing? And, how do you calculate the number of bottles being consumed in the 30th year?

Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate d = 0.05. Hence this person's goal is to maximize of40 e-0.05tu(c(t))dt = oſ40 e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e−0.05t(c(t))0.5 + A(− c(t)) + x(t)(dλ/dt). This person's wine consumption decreases at a
Transcribed Image Text:Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person's utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate d = 0.05. Hence this person's goal is to maximize of40 e-0.05tu(c(t))dt = oſ40 e-0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e−0.05t(c(t))0.5 + A(− c(t)) + x(t)(dλ/dt). This person's wine consumption decreases at a
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