Handi Inc. Options Contract Management

I need Help with the L(z) score in the middle.

 Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via “an  options supply contract”. At the start of quarter 1 (Q1) Handi pays LCD $15 per option. At that  time Handi’s forecast of demand in quarter 2 (Q2) is normally distributed with mean 15,000  and standard deviation 5,000. At the start of Q2 Handi learns exact demand for Q2 and then  exercises options at the fee of $45 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 for $80 per unit. a. How many optimum options should Handi purchase from LCD, Inc. at the start of Q1 to  minimize expected total procurement cost?  b. What is the chance that there is a need to procure at the spot market with only 7500  options signed? c. Compute Expected Total Procurement Cost with 10,000 options. 

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