Question

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 p_i, 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.

Please help show work please

Answer 1

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