PRINTABLE VERSION Practice Test 2 Question 1 Suppose you buy a piece of office equipment for $16,000.00. After 5 years you sell it for a scrap value of $5,000.00. The equipment is depreciated linearly over 5 years. The rate of depreciation for the piece of equipment is a) $2,200.00 per year b) $1,571.43 per year c) $3,200.00 per year d) $1,833.33 per year e) $11,000.00 per year f) None of the above. Question 2 A manufacturer has a monthly fixed cost of $100,000.00 and a production cost of $8 for each unit produced. The product sells for $21 per unit. The cost function for this situation is a) b) c) d) e) f) None of the above. Question 3 A company has fixed monthly expenses of $70,000.00 and production costs of $23 per unit produced. They sell their product for $25. What is their profit on the production and sale of 13,000 units? a) -$57,000.00 b) $36,000.00 c) -$44,000.00 d) $306,000.00 e) $325,000.00 f) None of the above. Question 4 A manufacturer has a monthly fixed cost of $80,000.00 and a production cost of $21 for each unit produced. The product sells for $33 per unit. Find the break-even point. a) b) c) d) e) f) None of the above. Question 5 Write the augmented matrix corresponding to the given system of equations: (Note: The dotted vertical line in each matrix below should be a single vertical line.) a) b) c) d) e) f) None of the above. Question 6 Which of the following matrices are in row-reduced form? (Note: The dotted vertical line in each matrix should be a single vertical line.) I. II. III. a) None of them b) II and III only c) All of them d) I only e) I and II only f) None of the above. Question 7 Use the Gauss-Jordan elimination process on the following system of linear equations to find the value of x. a) b) c) d) e) f) None of the above. Question 8 Use the Gauss-Jordan elimination process on the following system of linear equations to find the value of z. a) b) c) d) e) f) None of the above. Question 9 Use Gauss-Jordan elimination process to solve the following system of linear equations. a) b) c) d) e) f) None of the above. Question 10 Use Gauss-Jordan elimination process to solve the following system of linear equations. a) b) c) d) e) f) None of the above. Question 11 Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution(s) to the system, if they exist. (Note: The dotted vertical line in the matrix above should be a single vertical line.) a) b) c) d) e) f) None of the above. Question 12 Given A = a) 3X5 b) 15 c) 5X3 . What is the size (dimension) of A? d) 5X4 e) 4X3 f) None of the above. Question 13 Given A = a) b) c) d) e) f) None of the above. Question 14 . Find its transpose. Perform the indicated operation, if possible. a) b) c) d) e) f) None of the above. Question 15 Solve for x. a) b) c) d) e) f) None of the above. Question 16 Let A = and B = a) b) c) d) e) f) None of the above. Question 17 Find the inverse of the given matrix, if it exists. . Compute the product AB, if possible. a) b) c) d) e) f) None of the above. Question 18 Solve the following system of equations by using the inverse of the coefficient matrix. a) x = 2, y = 3 b) x = -5, y = 2 c) x = -9, y = 3 d) x = -7, y = -2 e) x = -4, y = 0 f) None of the above. Question 19 A certain academic department at a local university will conduct a research project. The department will need to hire graduate research assistants and professional researchers. Each graduate research assistant will need to work 26 hours per week on fieldwork and 14 hours per week at the university's research center. Each professional researcher will need to work 11 hours per week on fieldwork and 29 hours per week at the university's research center. The minimum number of hours needed per week for fieldwork is 154 and the minimum number of hours needed per week at the research center is 131. Each research assistant will be paid $257 per week and each professional researcher will be paid $402 per week. Let x denote the number of graduate research assistants hired and let y denote the number of professional researcher hired. The department wants to minimize cost. Set up the linear programming problem for this situation. a) b) c) d) e) f) None of the above. Question 20 Use the method of corners to maximize P = 49x + 26y subject to 2x + y< 9 0x + 3y< 9 x> 0 y> 0 a) The maximum occurs at ( 2 , 5 ) where P = 228. b) The maximum occurs at ( 5 , 0 ) where P = 245. c) The maximum occurs at ( 1 , 5 ) where P = 179. d) The maximum occurs at ( 2 , 6 ) where P = 254. e) The maximum occurs at ( 3 , 3 ) where P = 225. f) None of the above