FISHERY BULLETIN: VOL. 69. NO. 1 



60 



40- 



20- 



-O Totol run of 

 enfify 2mQles 



-• Cotch ollocation 



of linear program nriodel 



-A Actual catch 



allocation of I960 



<: 



8 



10 

 Day of season 



Figure 4. — Year 1960 large male catch allocations 

 (entity 3). The actual catch allocations are the 

 smoothed average values obtained from Royce (1965). 



— ^ Catcti allocation of linear program model 

 — o Totol run of entity 3 females 

 I000-] —A Actual cotch allocotion of I960 



5 10 



Doy of season 



8 



Figure 5.— Year 1960 small female catch allocations 

 (entity 3). The actual catch allocations are the 

 smoothed average values obtained from Royce (1965). 



we can observe various properties of the op- 

 timally allocated catches. For example, in Fig- 

 ures 3 and 4, the catch allocation of the early- 

 season is identical to the number of fish in the 

 run. These large male and large female fish 

 are more valuable than the smaller fish and 

 most valuable in the early part of the season 

 because of the value function. Hence, all the 

 large fish available are caught until the season's 

 limit for each of the large-fish entities has been 

 reached. We must be cautious here, however, 

 because as we point out in our discussion, there 

 is a possibility of modifying the characteristic 

 of the run by selective fishing. 



In order to interpret Figures 5 and 6, we must 

 realize that the next most valuable fish are the 

 small females. The difference in price between 

 small females and small males increases through 

 the season. This owes to the fact that small 

 females weigh less than small males and thus 

 decrease in value less towards the end of the 

 season. (Recall that the small females are more 

 valuable than small males only because of the 

 eggs which they contain.) We have assumed 

 that the value of the eggs is constant through- 

 out the season. 



The optimal solution shows that the cannery 

 is at capacity from days 4 to 10 with as many 

 small males being caught through day 6 as are 

 available, and as many additional small females 

 being caught as the cannery can process. On 

 days 7 to 9 there are enough fish exclusive of 

 the small females to bring the cannery to ca- 

 pacity. However, by day 10, the season's limit 

 of small males has been caught and small fe- 

 males must be caught to keep the cannery at 

 capacity. It must be remembered that the price 

 difference between females and males is greater 

 later in the season. For example, if a small 

 female is caught instead of a small male on the 

 6th day of the season, the increased profit is 

 $1,430 — $1,337 = $0,093, where the figures 

 are the value of small females and small males, 

 respectively, on day 6 for the logistic value 

 function which we used. But if a female is 

 caught instead of a male on day 10, the increased 

 profit is $1,371 — $1,270 ~_ $0,101, for the same 

 value function. Hence, while the cannery is be- 

 ing operated to capacity and since the total num- 



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