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 bottlesover 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) iseach 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 ofbottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = c(t): the stock of remainingbottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonianexpression yields: H = e-0.05t(c(t))0.5 + λ(− c(t)) + x(t) (dλ/dt). This person's wine consumption decreases at acontinuous rate of 15.60percent per year. The number of bottles being consumed in the 30th year isapproximately200.00(NOTE: Write your answers in number format, rounding to tens (whole

Given, Someone inherited 2,000 bottles. She intends to drink these over the next 40 years. Utility function : u(c(t))=(c(t))0.5 Future discount rate of conusmption =δ=0.05 We need to find the continuous rate in percent per year of a person's wine consumption decreasing. And to calculate the number of bottles being consumed in the 30th year.The rate at which the bottles are consumed is calculated as follows : Bottles consumed per year =200040=5050 bottles are consumed in a year Utility = 0.5×50 = 25Given, rate =0.05Every year bottles are added, 2000×5/100×40=4000Now, rate = 0.05=0.05×0.5=0.025Therefore, the consumption decreases at a rate of 25×0.025×25=15.6The number of bottles consumed in the 30th year We know, rate =15.6Number of bottles consumed in the 30th year = 2000×5100×10=1000or40001000=4 bottlesTherefore, Number of bottles in the 30th year is : Bottles consumed per year×4=50×4 =200 bottles