# How to use Maximum Sustainable Yield concept with given a given population, growth rate and carrying capacity?

For my class, I was given a hypothetical situation that uses the concept of Maximum Sustainable Yield to see how much fish I should harvest. I am given an initial population, a growth rate, and a carrying capacity.

Then with these given values, I was supposed to use this information to calculate for next year's population which I easily did with the logistic growth formula. I got a population of 368 (which is obviously rounded to a whole number). From what I know, with this initial population of 368 that I calculated, it would a bit over the one-half capacity but not over the carrying capacity of the environment that was given to me.

At this point, I don't know how to apply the Maximum Sustainable Yield concept here. I am not sure on how much I should harvest this year if the current fish population is 368. I don't want to harvest all 368 fish because that would mean that I wiped out the entire population for this year, correct? So would it make sense if I harvested half this number while still have enough fish for next year?

I tried to look at this graph I found as a reference but I'm not too sure how to apply it:

If I am made a misstep in my process, please do share. Thank you!

• I flagged the flag as off-topic because it is a mathematical homework question. Equally, the homework question "Albert earns 600 EUR per week and get's an annual bonus of 2000 EUR. Bart earns 2760 EUR per month. Who earns more per year?" does not fit to Economics.SE although it is about payment. Feb 12, 2018 at 8:36
• @daniel.neumann Personally I think it's on topic because the OP seems to be struggling with MSY concept and we can help with that. I do agree that the exact outcome has less relevance here. Feb 12, 2018 at 13:26
• @THelper: Thank you (for your answer below)! I think I understand how much I should harvest now since I do have the necessary values (K) to figure out how much there would be at K/2. From here, I believe I know the approximate number of fish to harvest without going below one-half capacity. Feb 12, 2018 at 18:38