Problem 1:
A farmer owns 6 rabbits. At the end of each year, a decision is made as to how many to sell or keep. In each year, the farmer can sell at most 10 rabbits. The profit from selling a rabbit in year i is pi, where p1 = $15, p2 = $20 and p3 = $12. The rabbits kept in year i will double in number in year i +1. Determine the maximum profit in the first 3 years and the optimal strategy.
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Answer :-
Given data:-
A farmer owns no.of rabbits = 6 rabbits.
The farmer can sell at most no.of rabbits = 10 rabbits
profit from selling a rabbit in year i =
Here, = $15,
= $20
and, = $12
The rabbits kept in year i will double in number in year = i +1
Now, we have to find out the:-
Determine the maximum profit in the first 3 years and the optimal strategy :-
We know, the formula for maximum profit in the first 3 years is,
Maximum profit in the first 3 years = * * (No.of rabbits ) [ i= 3 years ]
= * * 6
= ($12) * ( 8) * ( 6 )
= ($12) * ( 48 )
= $ 576
Maximum profit in the first 3 years = $ 576
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