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A fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water, the average weight of each fish will be W (n) = 500 – 2n, measured in grams. What is the value of n that will maximize the total fish weight after one season? Hint: Total Weight = numbers of fish | average weight of a fish.

A fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water, the average weight of each fish will be W (n) = 500 – 2n, measured in grams. What is the value of n that will maximize the total fish weight after one season? Hint: Total Weight = numbers of fish | average weight of a fish.

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
total wt. T = n(500-2n) = 500n - 2n^2 

T ' = 500 - 4n, & T " = -4, ie -ve, so setting T ' to zero will give a maxima 

500 - 4n = 0 

n = 125 g 

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