Wine storage,A retailer has bought several cases of a certain imported 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 possible profit?
SB // Dec 28, 2010 at 4:39 am
You might want to check the equation for the selling price of the wine. Your equation (53-10x) is a linear equation with negative slope. As written, the best time to sell the wine is NOW, as it’s value only goes down with time.
Using your equations the selling prive minus storage costs is
53-10x -3x = 53 – 13x
The max value is $53 when x = 0 years.