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2140_Test_3_review_solutions_fall_07

# 2140_Test_3_review_solutions_fall_07 - MATH 2140 TEST 3...

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MATH 2140 TEST 3 REVIEW SOLUTIONS 1. a. What equations in 1 x and 2 x are represented by the matrix: 1 3 5 3 1 5 - - - - 1 2 1 2 1 3 5 3 1 5 x x x x - =- - - = b. Use row operations (and SHOW the row operations you did) to put the matrix in part (a) into reduced row echelon form. And state the solution. 1 2 2 2 2 2 1 1 1 3 5 3 1 5 3 1 3 5 0 10 10 1 3 5 0 10 10 1 10 1 3 5 0 1 1 3 1 0 2 0 1 1 R R R R R R R R - - - - + - - - - - - - - - ° - - + - x1 = -2 x2 = 1

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2. A transportation company in charge of public school busses is trying to determine how many of each type of three busses to use per day. After considering wear and tear on the busses, they came up with a system of linear equations to be met where 1 x = number of small busses, 2 x = number of medium busses, and 3 x = number of large busses. After putting the system into reduced row echelon form, they obtained the following result: 1 0 1 5 0 1 2 6 0 0 0 0 - a. State all possible solutions. 3 2 1 6 2 5 x t x t x t = = - = + where t can equal 0, 1, 2, or 3 busses 3 2 1 0.. arg .. 6 2(0) 6.. .. 5 (0) 5.. ... x l e busses x med busses x small busses = = - = = + = OR 3 2 1 1.. arg ... 6 2(1) 4... .. 5 (1) 6 .... x l e busses x med busses x smallbusses = = - = = + = OR 3 2 1 2.. arg ... 6 2(2) 2.. ... 5 (2) 7.. ... x l e busses x med busses x small busses = = - = = + = OR 3 2 1 3... arg .... 6 2(3) 0 .... .... 5 (3) 8 ...... ..... x l e busses x med busses x small busses = = - = = + = b. Suppose that the daily costs for operating each of these three busses are \$180 per small bus, \$225 per medium bus, and \$325 per large bus. Determine and verify which solution (with units) that would result in the minimum cost?
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2140_Test_3_review_solutions_fall_07 - MATH 2140 TEST 3...

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