*What should be the amount of cod caught (in pounds) in such a way that it maxim
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*What should be the amount of cod caught (in pounds) in such a way that it maximizes the expected average daily gain?
OPERATIONS AT CONLEY FISHERIES, INC. Clint Conley, president of Conley Fisheries, Inc., operates a fleet of fifty cod fishing boats out of Newburyport, Massachusetts. Clint's father started the company forty years ago but has recently turned the business over to Clint, who has been working for the family business since earning his MBA ten years ago. Every weekday of the year, each boat leaves early in the morning, fishes for most of the day, and completes its catch of codfish (3,500 lbs. of codfish) by mid-afternoon. The boat then has a num- ber of ports where it can scll its daily catch. The price of codfish at some ports is very uncertain and can change quite a bit even on a daily basis. Also, the price of codfish tends to be different at different ports. Furthermore, some ports have only limited demand for codfish, and so if a boat arrives relatively later than other fishing boats at that port, the catch of fish cannot be sold and so must be disposed of in ocean waters. To keep Conley Fisheries' problem simple enough to analyze with ease, assume that Conley Fisheries only operates one boat, and that the daily operating expenses of the boat are$10,000 per day. Also assume that the boat is always able to catch all of the fish that it can hold, which is 3,500 lb. of codfish. Assume that the Conley Fisheries' boat can bring its catch to either the port in Gloucester or the port in Rockport, Massachusetts. Gloucester is a majorport for cod fish with a well-established market. The price of codfish in Gloucester is $3.25/lb and this price has been stable for quite some time. The price of codfish in Rockport tends to be a bit higher than in Gloucester but has a lot of variability. Clint has esti mated that the daily price of codfish in Rockport is Normally distributed with a The port in Gloucester has a very large market for cod and so Conley Fish- eries never has a problem selling their codfish in Gloucester. In contrast, the port in Rockport is much smaller, and sometimes the boat is unable to sell part or all of its daily catch in Rockport. Based on past history, Clint has estimated that the demand for codfish in Rockport that he faces when his boat arrives at the port in Rockport obeys the discrete probability distribution depicted in Table 5.1 It is assumed that the price of codfish in Rockport and the demand for codfish in Rockport faced by Conley Fisheries are independent of one another. Therefore, there is no correlation between the daily price of codfish and the daily demand in Rockport faced by Conley Fisheries At the start of any given day, the decision Clint Conley faces is which port to use for selling his daily catch. The price of codfish that the catch might command in Rockport is only known if and when the boat docks at the port and negotiates with buyers. After the boat docks at one of the two ports, it must sell its catch at that port or not at all, since it takes too much time to pilot the boat out of one port and power it all the way to the other port. Clint Conley is just as anxious as any other business person to earn a profit. For this reason, he wonders if the smart strategy might be to sell his daily catch in Rock port. After all, the expected price of codfish is higher in Rockport, and although the Demand TABLE 5.1 (lbs. of codfish) Probability Daily demand in Rockport faced by 1,000 Conley Fisheries 3,000 4,000 5,000 6,000 0.20Explanation / Answer
As per the information, clint can only sell that much in rockport which is demanded by them. Clint's sales at Rockport is dependent on Rockport's demand.
E.g. If rockport's demand is 4000 and
a) if he catches 3500. He can sell only 3500 and will lose an opportunity of 500 qty
b) if he catches 4000. He can sell all of 4000. this is ideal
c) if he catches 4800. He can sell 4000 and will throw the 800 away.
That is he can sell only the lesser of the two "his catch" or "rockport demand". He should be having a crystal ball to predict the rockport demand so that if requires he will catch 4000, if it requires 3800 he will catch 3800. But this is impossible as the demand is not known beforehand
Since we don't know what is the cost involved in catching the COD, we will assume it is same for 1 cod against 6000 cod. So Clint should not miss any demand. Therefore catch 6000 cod everyday. So that if it is 0, his 6000 wont cost anything but if it is 6000 demand, then he will fulfill all the demand
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