A = 70, B = 0.95, C = 1000
A typical fish farming process might involve placing small fish (fingerlings) in a dam, waiting for them to grow, and then harvesting all of the remaining fish.
People who rely on growing fish as a source of food are faced with the problem of working out when is the best time to harvest the fish, because although the fish grow bigger as time passes, unfortunately some of them die before they are harvested for food.
Data was collected and analysed for a particular species of fish. The following information was obtained:
Fish Length
The following formula gives a relationship between the fish length (L) in centimetres and time elapsed (t) in months since the fingerlings were placed in the dam:
L = A (1 – Bt )
Fish Weight
The following weight-length data is available for the species concerned:
| Length (cm) | 10.1 | 25.0 | 32.6 | 35.4 | 43.8 | 45.5 | 55.7 |
| Weight (g) | 15 | 236 | 520 | 660 | 1250 | 1425 | 2590 |
Length of Life
For every ‘C’ fingerlings of this species of fish placed in the dam, the number, n, still alive after t months is given by the formula:
N = C x Bt
Based on this information, find the best time to harvest all of the fish remaining in the dam in order to get the maximum weight of live fish. Validate your solution using technology.