Suppose there is a wine dealer who can decide to sell their stock now at a certain price or wait some length of time and potentially secure a higher value. The value of the wine at time t is given by the function V = ke 0.5 a) (4 points) Suppose the interest rate in the market is r. Using the value function V = ke 0.5t, write the present value of the wine in continuous time. b) (6 points) Derive the FOC for maximization and solve for the optimal value of t c) (10 points) Show that the solution you derived in part b) is indeed the optimal solution by showing that the SOC for optimization holds (Hint: here it is best to use a first derivative test for all of t 0).