Wine storage,A retailer has bought several cases of wine. As the wine ages, its value initially increases, but eventually the wine will pass its prime and its value will decrease. Suppose that x years from now, the value of a case will be changing the rate of 53-10x dollars per year. Suppose, in addition, that storage rates will remain fixed at per case per year. When should the retailer sell the wine to obtain the greatest profit?
hunchback // Dec 13, 2010 at 4:46 am
the rate of chg of profit is
dP/dx = 53 – 10x -3 = 50 – 10x
This is zero at x = 5, so that is where the profit curve has a stationary point.
To check if this is a min or max point:
d2P/dx2 = -10, which is < 0, so we do indeed have a max point.
The optimal time to sell the wine is after 5 years.