The number of mailings should the Canter send to each area of the country to get the responses it needs at least possible cost and the minimum cost where the Canter would like to poll at least 1500 democrats and 1500 republicans, each mailing to East coast gets responses from 100 democrats and 50 republicans, each mailing to Midwest gets responses from 100 democrats and 100 republicans and each mailing to West coast gets responses from 50 democrats and 100 republicans and mailings to East coast cost $ 40 each to produce and mail, mailings to Midwest cost $ 60 each to produce and mail and mailings to West coast cost $ 50 each to produce and mail.

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The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

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Chapter 6.4, Problem 27E

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To calculate: The number of mailings should the Canter send to each area of the country to get the responses it needs at least possible cost and the minimum cost where the Canter would like to poll at least 1500 democrats and 1500 republicans, each mailing to East coast gets responses from 100 democrats and 50 republicans, each mailing to Midwest gets responses from 100 democrats and 100 republicans and each mailing to West coast gets responses from 50 democrats and 100 republicans and mailings to East coast cost $40 each to produce and mail, mailings to Midwest cost $60 each to produce and mail and mailings to West coast cost $50 each to produce and mail.

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The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

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