options supply contract

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Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via an options type of supply contract . At the start of q uarter 1 (Q1) Handi pays LCD $20 per option. At that time Handis forecast of demand in Q2 is n ormall y distributed with mean 20,000 and standard deviation 8 000. At the start of Q2 Handi learns exact demand for Q2 and then exe rcises options at the fee of $4 0 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 Handis demand in Q2 be larger than the number of options held, Handi purchases additional di s plays on the spot market for $75 per unit.
a. Suppose Handi purchases 15 ,000 op tions. What is the probability that he will need to do procurement on the spot market?
b. Given that Handi purchases 15 ,000 options, what is the expected number of displays Handi will buy on the spot market?
c. Given that Hand i purchases 15 ,000 options, what is the expected number of options that Handi will exercise?
d. What is Handis expected total procurement cost given that he purchases 15 ,000 options?
e. What is the fill – rate Handi implies by purchasing 15 ,000 options?
f. How many options shou ld Handi purchase from LCD, Inc. ? (i.e. the optimum options)
g. What is Handis expected total procurement cost given the number of purchased options from part f ?
h. Suppose Handi were to procure exclusively from the spot market? What would be his expected procurement cost? What would be his fill – rate in this arrangement? Also, what is the mismatch cost he incurs with this arrangement?

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