Consider a wine dealer who has k bottles of wine. The dealer can sell them now (t=0) or can store it for some time and then sell them later. The value of k bottles at t-th month is given by Vt​=ket​ The dealer can use the sales revenue as principal in a risk-free investment at rate r. (a) (10) If the dealer sells them now, what is the sales revenue? (b) (10) Write out the present value PVt​ of k bottles at t-th month. (c) (10) State the first-order condition for optimal length of storage time. (d) (10) If the risk free rate is 5%, what is the optimal timing of sales? (e) (10) If the dealer sells them at the optimal timing, what is the present value of the sales revenue?