In the pursuit of happiness, Cooper decides that the coming season is his last season to sell Q-scanners. He forecasts the demand to be Poisson with a mean 4. Currently, he has two Q-scanners on hand (left from the previous season). The producer offers him two purchasing options: 

(i) buy at unit price $120,000 buy before the selling season; 

(ii) buy at unit price $200,000 before the end of the selling season, when Cooper knows demand precisely.

(a) To minimize the expected cost, how many units should Cooper order through option (i)?

(b) To fill 99% of orders with on-hand inventory, how many units should Cooper order through option (i)?

(c) If Cooper decides not to use either option, what is the fraction of demand he can satisfy?