Handi Inc., a maker of cellphones, procures a standard display from LCD Inc. via an options contract. At the start of quarter 1 (Q1) Handi pays LCD $3.5 per option. At that time Handi's forecast of demand in Q2 is Normally distributed with mean 24000 and standard deviation 6000. At the start of Q2 Handi learns exact demand for Q2 and then exercises options at a fee of $4.5 per option (for every exercised 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 at $12 per unit.

For example, suppose Handi purchases 30000 options at the start of Q1 but at the start of Q2 Handi realizes that demand is 35000 units. Then Handi exercises all of its options and purchases 5000 additional units on the spot market. If, on the other hand, Handi realized demand is 27000 units, then Handi only exercises 27000 options.

A) If Handi chooses to purchase 28,000 options, what is the probability that Handi needs to purchase displays from the spot market?

B) If Handi wants to maximize the profit, how many options should Handi purchase from LCD?

C) Suppose the price for the display on the spot market price changes to $8 per unit, how many options should Handi purchase from LCD to maximize the profit?