Part 1

You are currently working as inventory manager for "3 Onions and 6 Cabbages", a wholesaler in New Hampshire 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.

Currently, you order the mean demand. Any left over is thrown away at the end of the day. What is your expected units short and profit per day following this ordering strategy?

Expected units short

Provide your answer with three decimal places.

Expected profit

Part 2

After taking SC1x, you have realized that with your current strategy you are not maximizing profits. What should your daily order quantity be in order to maximize daily profits? What will your expected units short and expected profit values be?

Optimal order quantity

Expected units short

Expected profit

Part 3

You noticed that your reliability to provide supplies affects your future sales, "3 Onions and 6 Cabbages" will lose some customers when you stock out. You estimate the penalty of stocking out to be $24 per lb. What should your new optimal order size be? What will your expected units short and expected profit values be?

Optimal order size

Provide your answer with 2 decimal places.

Expected units short

Expected profit

Part 4

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) Probability

20 0.05

21 0.15

22 0.22

23 0.17

24 0.12

25 0.09

26 0.09

27 0.08

28 0.03

Optimal order size

Enter your answer as an integer.

Expected units short

Provide your answer with 3 decimal places.

Expected profit

Round your answer to the nearest integer.