Managers of the restaurant, NicePizzeria@Nola, have to plan for the number of pizzas they want to make at the beginning of each day.

Each pizza costs $3 to make and the price is $9 per pizza. Note: The profit for each pizza sold is $6. For the ones supplied but not sold, the profit is -$3.

Based on market research, the manager knows that the daily demand, denote as D, is a random variable that follows the following general discrete distribution.

Daily demand, D	Probability
20	0.05
25	0.15
30	0.30
35	0.25
40	0.20
45	0.05

1) Suppose we supply 40 pizzas, what is the expected profit? [ Select ] ["172.5", "107.5", "None of the above", "32.75"]

2) What is the expected daily demand, i.e., the expected value of D? [ Select ] ["32.75", "35.50", "32.50", "40.00"]

3) Denote FD(x) to be the cumulative distribution function of D, what is value of FD(30)? [ Select ] ["0.50", "0.30", "0.20", "0.45"]

4) Given the screenshot below, which is the excel formula that generates a random demand D, that follows the above general discrete distribution? [ Select ] ["VLOOKUP(1,A$2:B$7,2,1)", "VLOOKUP(RAND(),A$2:B$7,2,1)", "None of the above", "VLOOKUP(RAND(),B$2:C$7,2,1)"]