1 Fish farming problem. A fish farmer keeps fish in a single large tank. He has a contract to
supply a fixed number of fish at the end of each month for the period January to May. The
price he receives for the fish depends on the month and the size of the fish in the way shown in
the Table below:
SELLING PRICE
PENCE PER FISH
Month Length of fish (inches)
8 9 10 11 12
January 10 15 20 - -
February 8 10 14 20 24
March 4 6 10 14 20
April 2 4 8 14 20
May 0 2 8 14 22
At the beginning of January all the fish are 8 in long. Subsequently they can be fed at rates 1,
2 or 3 in each month. Feeding at rate 1 maintains a fish at its current size, feeding at rate 2
increases its size by one inch in one month and feeding at rate 3 increases its size by two inches
in one month. All the remaining fish must be fed at the same rate. The cost of feeding at the
various rates depends on the size of the fish in the way shown in the table below:
FEEDING COST
PENCE PER FISH
Length Rate
(inches) 1 2 3
8 1 2 5
9 3 4 7
10 5 6 7
11 8 9 -
12 10 - -
Determine the feeding policy which maximises the total return and the total return under that
policy.