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SMA_01

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dx/dt=r1x(1-x/K1)-α1xy

dy/dt=r2y(1-y/K2)-α2xy

Let

x= number of blue whales (measured in 100,000's)

y=number of fin whales (measured in 100,00's)

t=time measured in centuries

r=revenue obtained from harvesting (measured in 1,000,000 of dollars per year)

A blue whale carcass is worth $12,000 and a fin whale carcass is worth $6,000. Assuming that controlled harvesting can be used to maintain x and y at any desired level, what population levels will produce the maximum revenue? (Once population reaches the desired levels, the population levels will be kept constant by harvesting at a rate equal to the growth rate).

The equation without harvesting are

dx/dt=5x(1-x/1.5)-xy/10

dy/dt=8y(1-y/4)-xy/10

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I am a little unsure about my equation for revenue- more specifically, I don't know how to incorporate time.

I have r= 12,000x + 6,000y, but that doesn't seem right because I neglected t. So I thought maybe this is more accurate:

r=12,000 (x/100t) + 6,000 (y/100t) (since t is measured in centuries)

Is this correct? Or am I completely missing the point?