Pts a wine dealer contemplates when to sell his

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6. (5 pts) A wine dealer contemplates when to sell his bottle of wine for $30 today, or wait to sell it in the future.If he sells it in the future, then he can sell it for a higher price. However, the sooner he sells the bottle, the moretime he will have to invest the money (at 5% interest compounded continuously) and perhaps make a biggerprofit that way.The amount of money a wine drinker will pay for the bottletyears from now is 30(1 + 20t) dollars. When isthe best time for the dealer to sell his wine?(In this problem, you may use a calculator to do your computations, but aside of that, youmustshow allwork.For example, if solving for the critical numbers of a function, you must write the equation to set thederivative equal to 0. If there are endpoints necessary to test for the domain of your function, you must do so.The only thing you can use your calculator for is for carrying out computations or solving an equation which youhave explicitly written!)Solution:The dealer sells this 1 bottle at some pointtyears from now (t0) for 30(1 + 20t) dollars.However, given interest, what does 30(1+20t) dollars translate into in today’s terms? In order to find the idealtime for him to sell the wine, we need to maximize the present value of that future payment, which isf(t) below:f(t) = 30(1 + 20t)e-0.05t,t0.

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