The 7-Eleven store in Randwick sells fresh sushi boxes around lunch time. Around 7am in the morning, the store must submit an order for the sushi boxes to a catering company, which then delivers the order at around 11am (delivery is free of charge). Each sushi box costs 7-Eleven $3 and the retail price is $7. At the end of each day any unsold sushi boxes are donated and collected by a charity organisation. Assume the demand for the sushi boxes follows the following discrete distribution.

Demand d	50	60	70	80	90	100
Probability	0.05	0.15	0.20	0.30	0.20	0.10
F(d)	0.05	0.20	0.40	0.70	0.90	1.00

(a) Suppose the customers for the sushi box would buy their lunch at another convenience store across the street if 7-Eleven is out of stock. How many sushi boxes should the 7-Eleven store order in the morning to maximise its expected profit? (10 marks)

(b) Suppose that any customer unable to purchase the sushi box at the 7-Eleven store would settle for a snack box, which sells for $5 and costs the store $2.5 each box. Because the snack boxes are easily stored, the store never runs out of them. Assuming the store management is interested in maximising profits, how many sushi boxes should the store order in the morning? Briefly discuss the result. (10 marks)