ROTHSCHILD and BALSIGER: LINEAR-PROGRAMMING SOLUTION 



ious entities. The 1960 run had an escapement 

 of 31 billion eggs. We estimate that this escape- 

 ment was partitioned among the entities as 

 follows: 



Entity 1, 57.5 % or 8,136,000 fish escaping 

 Entity 2, 43.4 % or 210,000 fish escaping 

 Entity 3, 74.8 '~'r or 7,964,000 fish escaping 

 Entity 4, 30.8^; or 389,000 fish escaping 



It is interesting to note that in addition to 

 8,350,000 females which were estimated to have 

 escaped in 1960, there were, in addition, 

 8,300,000 males that escaped, signifying a nearly 

 1 : 1 sex ratio. 



Our general approach in presenting our par- 



ticular 1960 run example was to concentrate up- 

 on simulating the actual events in 1960 by using 

 the above run data in equations (13) and (7), 

 the fecundities listed in Table 2, and the lo- 

 gistic value function. We also present some 

 results where we effectively drop equation (13) 

 and replace it with equation (10) using a low 

 escapement of 5 billion eggs in order to dem- 

 onstrate the sensitivity of the model to various 

 escapement goals. 



In Figures 2, 3, 4, and 5, we depict the op- 

 timum allocation of the catch which we obtained 

 using the actual 1960 escapement data. The 

 figures also include the smoothed catches de- 

 rived from Royce's work. From these figures. 



Catch ollocotion of linear program model 

 Total run of entity 1 males 



120-1 



100- 





^ ^ Cotcfi ollocotion of 

 lineor program model 



o— — o Total run of entity 4 femoles 



A — ^ Actual catch allocation of 1960 



5 10 



Day of season 



15 18 



10 

 Day of season 



r 

 15 



18 



Figure 2. — Year 1960 small male catch allocations 

 (entity 1). The actual catch allocations are the 

 smoothed average values obtained from Royce (1965). 



Figure 3. — Year 1960 large female catch allocations 

 (entity 4). The actual allocations are the smoothed 

 average values obtained from Royce (1965). 



125 



