Math 211 Test 2 Practice Given the system of equations Use this to answer the first THREE problems x1 x2 x3 10 2 x2 x3 13 2 x1 3x2 11 1 2 Use Gaussian Elimination method to find the solution to the above linear system Show at least 5 row operation steps by hand using matrices You have to write each step i e row operation command and resulting matrix for full credit a Find the inverse of the coefficient matrix A using your calculator A 1 b 3 Use the inverse matrix to solve the system of equations Indicate the process you are using by showing your work Solve the same system using Cramer s find the determinants needed rule You may use your calculator to 4 Each matrix below is in the reduced row echelon form for the augmented matrix that represents a system of equations in x and y and z State how many solutions each system would have If the solution is unique list it if one has infinite number of solutions list two of them a 1 0 0 5 0 1 0 4 0 0 0 1 b 1 0 3 6 0 1 2 4 5 A box manufacturing plant makes two types of boxes each of which reqires time on the saw for cutting then time on the assembly and later for finishing Model A requires one hour of cutting 2 hours of assembly and one hour of finishing Model B requires one hour of cutting one hour of assembly and 3 hours of finishing There are 40 man hours available for cutting per week 60 man hours for assembly and 90 msnhours for finishing Suppose that the profit on model A box is 20 and the profit on model B box is 25 Maximize the weekly profit a Write down the profit function and the constraints for the problem b Graph the region and list all corner points to answer the question 6 A candy manufacturer makes 40 pounds of a snack mix which costs 1 5 a pound The mix has three components raisin that costs 1 a pound chocolate chips that costs at 2 a pound and nuts that costs 2 a pound In the mix there are 2 pounds more nuts than chocolate chips How many pounds of each component must be used to make the mixture Set up the system of linear equations and solve the problem
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