Question: A lake is to be stocked with smallmouth and largemouth bass. Let \(x\) represent the number of smallmouth bass and let \(y\) 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 \(W_{1}=3-0.002 x-0.005 y\), and the weight of a single largemouth bass is \(W_{2}=4.5-0.003 x-0.004 y\).

Assuming that no fish die during the six-month period, how many smallmouth bass and how many largemouth bass should be stocked in the lake so that the total weight \(T\) of bass in the lake is a maximum?

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