# MAT183-2006Fall - P RINT Y OUR F ULL N AME C IRCLE Y OUR I...

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PRINT YOUR FULL NAME CIRCLE YOUR INSTRUCTOR'S NAME Doerr Anderson Graver Griffin MAT 183 Final Exam Dec. 13, 2006 Ver. A Signature: Instructions: Write the answers and show the main steps of your work on this test sheet. There are 15 questions on 16 pages (including this cover). Be sure you have all 16 pages (8 sheets) and that they are all of the same version. You should spend no more than 7 minutes on each problem; be sure that you get to the easier parts of each problem. The Final Exam is scored on a basis of 100 points and will count 25% of your final grade. Where indicated, you must show your work to get full credit! DO NOT WRITE ON THE REST OF THIS COVER SHEET! Problem 1 Problem 7 Problem 12 Problem 2 Problem 8 Problem 13 Problem 3 Problem 9 Problem 14 Problem 4 Problem 10 Problem 15 Problem 5 Problem 11 Test 3 Total Problem 6 Test 2 Total Test 1 Total EXAM TOTAL :

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2 MAT 183 Final Exam Dec. 13,2006 Ver. A Problem 1 (4 points) In each case below, a system of three equations in x, y and z has been put in row-reduced echelon form. You are to interpret this matrix. In each case circle one of "No Solution", "Unique Solution" or "Many Solutions." If you circle "Unique Solution", fill in the values of x, y and z. (Order will be switched on different versions) a. [~ ~ .', ~2] o 0 0 0 No Solution Many Solutions Unique Solution x = y= z= No Solution Many Solutions Unique Solution x = y= z= No Solution Many Solutions Unique Solution x = y= z=
MAT 183 Final Exam Dec. 13, 2006 VeT. A 3 Problem 2 (7 points) A bank wishes to invest a \$250,000 trust fund in three sources: bonds paying 8% annually, CDs paying 7% annually and mortgages paying 10% annually. The bank wishes to realize an annual income of \$21,000 from this investment. A condition of the t'IUSt is that exactly ~ of the fund must be invested in bonds and CDs. How much should the bank invest in each category? Let b denote the amount invested in bonds; c the amount invested in CDs and m the amount invested in mortgages. a. (4 points) Give the system of equations that you plan to use. b. (3 points) Solve that system: b= c= m=

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4 MAT 183 Final Exam Dec. 13, 2006 Ver. A Problem 3 (7 points) Consider an industry with 3 sectors, E (energy), I (iron ore} and T (tmnsportation), represented by the following input-output matrix: At what production levels in billions of dollars should each sector operate to meet a demand of \$5 billion from sector E, \$2 billion from sector I and \$6 billion from sector T? a. (4 points) Write this problem as a matrix equation. b. (3 points) Fill in your answer (rounded off to two decimal places) E = \$ billion. I = \$ billion. • T = \$ billion.
5 .MAT 183 Final Exam Dec. 13, 2006 Vel'. A Problem 4 (8 points) A small computer store sells two types of computers, one for home use (H) and one for office use (0). The matrix [A] below represents the number of units of memoru (.M), USB ports (U) and external display ports (E) used on each type of computer. M

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## This note was uploaded on 06/17/2011 for the course MATH 183 taught by Professor Na during the Spring '09 term at University of North Carolina School of the Arts.

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MAT183-2006Fall - P RINT Y OUR F ULL N AME C IRCLE Y OUR I...

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