Scotch whisky increases in value as it ages, at least up to a point. For any period of time, t, the value of a barrel is given by V = 100t – 6t2. This function implies that the proportional rate of growth of the value of the scotch is (100 – 12t)/V.

a. Graph this scotch value function.

b. At what value of t is the barrel of scotch most valuable?

c. If the real interest rate is 5 percent, when should this distiller bottle the scotch for immediate sale?

d. How would the distiller's decision change if the real interest rate were 10 percent?