So here's the problem from the top:
Biology A lake is to be stocked with smallmouth and largemouth bass. Let represent the number of smallmouth bass and let represent the number of largemouth bass in the lake. The weight of each fish is dependent on the population densities. After a six-month period, the weight of a single smallmouth bass is given by
and the weight of a single largemouth bass is given by
.
Assuming that no fish die during the six-month period, how many smallmouth and largemouth bass should be stocked in the lake so that the total weight T of bass in the lake is a maximum?
Ok, so I'm not quite sure what to do with this problem. The rest of the section has been on taking first derivatives, finding critical points, and then using along with to determine if a specific point is a maximum, minimum, etc. I do know that it's looking for a maximum, so must be true and must also be true. Beyond that though, I'm not quite sure where to go...if I take the first partial derivative of either of those functions, I just get a constant...I'm assuming since it wants total weight that I do the same thing with each of the two equations and then add the answers together, however, I'm at a loss as to what specifically to do here.