A sushi shop makes fresh sushi daily in a multiple of 50 units. As they use fresh produce making a sushi cost $2.5 and they are sold to customers for $7.5. Sushi that was not sold during the day will be sold at $0.5 for a quick sale at the end of the day and they are always sold out. The sushi store has analysed data and has given its daily demand below:

Demand

100 = 10% probability

200 = 15% probability

300 = 25% probability

400 = 30% probability

500 = 15% probability

600 = 5% probability

1) Make a table of the expected profits or losses for each possible demand quantity to find out the optimal number of sushi that the store should make daily. Show your detailed calculations.

2) Confirm the optimal number of sushi that the store needs to make in one day, found in part 1 by comparing the expected profit or loss with those of the closest quantity that the sushi store can make above and below that optimal number. Show your detailed calculations

3) Confirm the optimal number found in part 1 by using a complete marginal analysis which shows the total costs of overestimating or underestimating demand for each quantity of sushi which the shop can produce based on the possible demands (not just based on cumulative probability). Show your detailed calculations.