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Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next three months. Each table will require 30 hours of labor, each will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of wood to make, and a chair requires 15 board feet. A table earns the couple $575 in profit, and a chair earns $120 in profit. Most people who buy a table also want four chairs to go with it, so for every table that produced at least four chairs must also be made, although additional chairs can also be sold separately. Formulate and solve an integer programming model that will determine the number of tables and chairs the Jacobsons should make to maximize profit.
Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x
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Calculate an exponentially smoothed forecast, using an alpha value of .30.
Calculate the mean and variance of the new observations
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Use mathematical induction to solve the equation.
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Explain how you decide whether it is easier to solve a system by substitution or the elimination method. Response should be detailed and include an example
The temperature(at a randomly selected time) is normally distributed with mean 83 degrees Fahrenheit and standard deviation 5 degrees. Find the following probabilities:
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