You are currently working as inventory manager for "9 Artichokes and 6 Eggplants", a wholesaler in Washington specialized in organic, locally produced vegetables. You maintain a record of the quantity, in pounds, of the demand of vegetables per day. You have determined that the demand approximate a normal distribution with a mean of 22.55 and a standard deviation 2.64. You buy the vegetables at $12 /lb and sell them at $51 /lb.

You decided to check the empirical distribution of the demand. In your record (the table below), demand has been rounded up to the nearest pound (lb).

Based on this empirical distribution, what is the new optimal Q assuming that, like in Part 3, there is stock out penalty of $24? What are your new expected units short and expected profit values? (For Part 4, you may assume that the vegetables are supplied, consumed and resold in discrete pound (lb) units.)

Demand (lb) 20 21 22 23 24 25 26 27 28

Probability 0.05 0.15 0.22 0.17 0.12 0.09 0.09 0.08 0.03