final_210

# final_210 - Practice FINAl TEST 1 A furniture manufacturer...

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Practice FINAl TEST 12/08/2008 1 A furniture manufacturer makes tabels, chairs, and sofas. In one month, the company has available 300 units of wood, 350 units of labor, and 225 units of upholstery. The manufactuere wants a production schedule for the month that uses all of these resources. The diFerence products require the following amounts of the resources. Table Chair Sofa Wood 4 1 3 Labor 3 2 5 Upholstery 2 0 4 Set up and solve the system of equations to determine how much of each product should be manufactured(using the LU decomposition). 2 The matrix B p 2 3 - 1 3 - 1 3 2 3 P is the inverse of A p 2 1 1 2 P (a) Verify that u 1 = [1 , 1] and u 2 = [1 , - 1] are eigenvectors of both A and B. (b) Determine the eigen values of A and B. How are the eigenvalues of A and B related? 3 Solve the second-order diFerential equation by matrix form.(you must ±nd eigenvalues and eigenvectors.) The initial condition is x (0) = 10 , y (0) = 10. y

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final_210 - Practice FINAl TEST 1 A furniture manufacturer...

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