Suppose that an insect population, r(t), is controlled by a natural predator population,y(t).(a) Write down a predator-prey model describing the interaction of these two populations.(b) Suppose an insecticide is used to reduce the population of insects, but it is also toxicto the predators; hence, the poison kills both predator and prey at rates proportionalto their respective populations. Modify your model from (a) to take this into account.

Given Data: (a) To Write down a predator-prey model describing the interaction of these two…

Answered: Suppose that an insect population,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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This is System Modeling & Simulation question
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
Find the market equilibrium price for the demand function D(X) = 2x? – x + 6 And the supply function S(X) = 4x2 + 3x
A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.
2. Linearize the following equation about the equilibrium point (xo, Yo, Zo, uo) * = a X 1+ y² + c y = yu z = xy + u Where z is the output, u is the input and a and care constant.
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. D(x) = e X+2 S(x) = e x-6 a) Find the equilibrium point. b) Find the consumer surplus at the equilibrium point. c) Find the producer surplus at the equilibrium point. a) What are the coordinates of the equilibrium point? (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Do not include the $ symbol in your answer)
D(x) is the price, in dollars per unit, that consumers will pay for x units of an item, and S(x) is the price, in dollars per unit, that producers will accept for x units. Find a) the equilibrium point, b) the consumer surplus at the equilibrium point, and c) the producer surplus at the equilibrium point if: D(x)=(x-7)², S(x)=x² + 8x + 5
number of people who will be infected by t = 12 days. 7. Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that high a population level. a. Discuss the following model for the whale population dP dt = k(MP)(Pm) where P (t) denotes the whale population at time t and k is a positive constant. b. Graph dP/dt versus P and P versus t. Consider the cases in which the initial population P(0) = Po satisfies Po
Suppose the inverse market demand function is P = 20 −Q and the total cost function is TC = Q2.1.1. If the market only has one firm, what would be the monopoly output and profit?1.2. If the market has two symmetric firms (each with the total cost function C = Q2), what is the Cournot equilibrium quantity and profit?1.3. If there are two symmetric firms as in 1.2, what level of output for each firm would maximize the total industry profit? Why is this total profit different than in 1.1? Suppose the two firms in 1.3 engage in Cournot competition for just one period. Show that the output levels in 1.3 are not sustainable in a collusion. Suppose the two firms in 1.3. engage in Cournot competition for infinitely many periods. What is the lowest discount factor δ that would sustain the output levels in 1.3 in a collusion using the grim trigger strategy?

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