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 8 = 0.05. Hence this person's goal is to maximize of40 e-0.05tu(c(t))dt = 0/40 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 + XA(- c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a continuous rate of 15.60 percent per year. The number of bottles being consumed in the 30th year is

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See attachment. This is not a writing assignment. I need to understand the mathematical steps to calculate the continuous rate of wine consumption, and also the number of wine 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 = 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 + λ(− c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a
continuous rate of 15.60
percent per year. The number of bottles being consumed in the 30th year is
approximately
200.00
(NOTE: Write your answers in number format, rounding to tens (whole
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 = 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 + λ(− c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at a continuous rate of 15.60 percent per year. The number of bottles being consumed in the 30th year is approximately 200.00 (NOTE: Write your answers in number format, rounding to tens (whole
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