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BDH Environmental Management 216 Ware Blvd. Mercer, NY 33002 January 24, 2011 Stetson Modeling 1400 Coleman Ave. Macon, GA 31117 Dear Associates: As you may know, BDH Environmental Management has inthe past year expanded its immensely successful fish farms along the scenic Tonwathing coast near Leseatt to include a large lake near Lonlinc—therefore allowing us to also supply Lonlinc and surroundswith a needed and ecologically sound food source supplied fresh daily by our exclusively electric fleet of bright blue delivery vans. The success of this endeavor we credit primarily to a carefulmathematical analysis carried out by your company last year. In an effort to keep up with the demand that we have discovered in the Lonlinc area we are beginning a second farm near Haoma. As is ourpractice, we first seeking a theoretical basis for the initial stocking of the lake. During this phase of our operations we are stocking the lake with fish at regular intervals. We have found in the past thatbecause of the disorientation of the fish being introduced to a new environment and the nature of the process of their introduction, the population of fish in the lake is changed little by breeding andmust therefore be built up by sequentially adding more fish. Once a sufficient fish population exists in the lake the farm will become self sustaining. We will be able to introduce fish in the new lakeat a rate of 300 fish/2 months. During the time during which they are being introduced, however, the population decreases (due to the imposition of predators) at a rate that is, for small populations,proportional to the number of fish present, with an experimentally determined constant of proportionality k1 = 4 × 10−4 (fish/day)/fish. For larger populations the population decreases due to predatorsproportional to the square of the fish population, with constant of proportionality k2 = 1 × 10−5 (fish/day)/fish2 . Initially, of course, there are no fish in the lake. Given this information, we need...
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