Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via an options contract. At the start of quarter 1 (Q1), Handi pays LCD $4.50 per option. At that time, Handi's forecast of demand in Q2 is normally distributed with mean 24,000 and standard deviation 8,000. At the start of Q2, Handi learns exact demand for Q2 and then exercises options at the fee of $3.50 per option, (for every exer- cised option, LCD delivers one display to Handi). Assume Handi starts Q2 with no display inventory and displays owned at the end of Q2 are worthless. Should Handi's demand in Q2 be larger than the number of options held, Handi purchases additional displays on the spot market for $9 per unit. For example, suppose Handi purchases 30,000 options at the start of Q1, but at the start of Q2 Handi realizes that demand will be 35,000 units. Then Handi exercises all of its options and purchases 5,000 additional units on the spot market. If, on the other hand, Handi realizes demand is only 27,000 units, then Handi merely exercises 27,000 options.
a. Suppose Handi purchases 30,000 options. What is the expected number of options that Handi will exercise?
b. Suppose Handi purchases 30,000 options. What is the expected number of displays Handi will buy on the spot market?
c. Suppose Handi purchases 30,000 options. What is Handi's expected total procurement cost?
d. How many options should Handi purchase from LCD?
e. What is Handi's expected total procurement cost given the number of purchased options from part d?