A grocer is selling Halloween themed candy. Because of the markup due to the holiday', the grocer is able to sell large bags of candy for $8 per bag the week before Halloween. The grocer is able to procure the large bags of candy from their supplier for $3 dollars per bag, but they must place in advance. If the grocer runs out of large candy bags to sell, it will be impossible to get more the week of Halloween. On the other hand, any large bags of Halloween-themed candy that are leftover after Halloween can be sold for the markdown price of $2.50 per bag. Based on historical data, the grocer believes that the total demand for large candy bags for the week before Halloween is 150 dozen with probability 1/10, 200 dozen with probability 3/10, 250 dozen dozen with probability 2/10, 300 dozen with probability 3/10, and 350 dozen with probability 1/10. Assume that that the grocer's goal is to maximize expected profit. (a) What is the mean demand for large bags of candy in bags? (b) If 200 bags are procured by the week before Halloween, what is the expected profit? (C) What is the smallest amount (among possible orders of 150 bags, 200 bags, 250 bags, 300 bags, and 350 bags) to cover demand at least 80% of the time? That is, what is the smallest q* such that Pr(D 80% (d) What is the best amount of large candy bags for the grocer to procure by the week before Halloween? (e) In what sense is that amount optimal? In other words, what was your objective function? (f) Instead, suppose that the demand was normally distributed with mean 500 bags and variance 50 bags?. How many large candy bags should be ordered?