FALL 2012 MATH 1324 REVIEW EXAM 2

Size: px

Start display at page:

Download "FALL 2012 MATH 1324 REVIEW EXAM 2"

Ann Patterson
5 years ago
Views:

1 FALL 0 MATH 3 REVIEW EXAM MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the order of the matri product AB and the product BA, whenever the products eist. ) A is, B is. AB is, BA is noneistent. AB is, BA is. AB is, BA is. AB is noneistent, BA is. ) ) A is, B is. AB is, BA is. AB is, BA is. AB is noneistent, BA is noneistent. AB is, BA is. ) Given the matrices A and B, find the matri product AB. 3) A = - 3, B = 0 - Find AB. -3 AB is not defined ) ) A = 3-0, B = 30-0 Find AB. ) 0-6 AB is not defined

2 ) A = 3-0 -, B = 0-3 Find AB. AB is not defined ) Determine whether the two matrices are inverses of each other b computing their product. 6) 3 and Yes No 6) 7) - -7, - 7-7) No Yes ) - -, ) No Yes Find the inverse, if it eists, of the given matri. 9) A = ) ) A = ) 3-3 No inverse

3 Solve the problem. ) Three different high schools plan to order the same three tet books. School A plans to order of book, 0 of book, 30 of book 3. School B plans to order 0 of book, 70 of book, 30 of book 3. School C plans to order 0 of book, 90 of book, 30 of book 3. The cost of book is $ per cop, the cost of book is $0 per cop, and the cost of book 3 is $ per cop. What matri product displas the cost to each school of buing the tetbooks? Displa the two matrices which must be multiplied and their product = = = = ) Solve the matri equation for X. ) A = 3, B = -6 -, AX = B ) ) A = , B = , AX = B 3) Solve the sstem b using the inverse of the coefficient matri. ) + + z = - + z = z = -3 ) No solution (, -, ) (-,, ) (,, -) Write a sstem of equations and use the inverse of the coefficient matri to solve the sstem. ) A compan makes 3 tpes of cable. Cable A requires 3 black, 3 white, and red wires. Cable B requires black, white, and red wires. Cable C requires black, white, and red wires. The used 0 black, white and 90 red wires. How man of each cable were made? ) cable A 3 cable B 0 cable C cable A 30 cable B 93 cable C cable A 30 cable B 0 cable C 0 cable A 93 cable B cable C Graph the linear inequalit. 3

4 6) 3 + 6)

5 7) 3 7)

6 Graph the feasible region for the sstem of inequalities. ) )

7 9) )

8 0) )

9 ) )

10 A manufacturer of wooden chairs and tables must decide in advance how man of each item will be made in a given week. Use the table to find the sstem of inequalities that describes the manufacturerʹs weekl production. ) Use for the number of chairs and for the number of tables made per week. The number of work-hours available for construction and finishing is fied. ) Hours per chair Hours per table Total hours available Construction Finishing ) Use for the number of chairs and for the number of tables made per week. The number of work-hours available for construction and finishing is fied. 3) Hours per chair Hours per table Total hours available Construction 3 7 Finishing Find the value(s) of the function on the given feasible region. ) Find the maimum and minimum of z = ), 7, 70 70, 7, 7

11 ) Find the minimum of z = + 3. ) Use graphical methods to solve the linear programming problem. 6) Maimize z = subject to: ) - - Maimum of 3 when = 3 and = Maimum of when = and = 0 Maimum of 3 when = and = 3 Maimum of when = and =

12 7) Minimize z = subject to: ) - - Minimum of.0 when = and = 3 Minimum of. when = and = Minimum of.0 when = 3 and = Minimum of.6 when = 9 and = Find the value(s) of the function, subject to the sstem of inequalities. ) Find the minimum of P = subject to: 0, 0, +. ) 3 66 State the linear programming problem in mathematical terms, identifing the objective function and the constraints. 9) A firm makes products A and B. Product A takes 3 hours each on machine L and machine M; product B takes hours on L and 3 hours on M. Machine L can be used for hours and M for 6 hours. Profit on product A is $9 and $6 on B. Maimize profit. 9) Maimize 9A + 6B Subject to: 3A + 3B 3A + B 6 A, B 0. Maimize 9A + 6B Subject to: 3A + 3B 3A + B 6 A, B 0. Maimize 6A + 9B Subject to: 3A + 3B 3A + B 6 A, B 0. Maimize 9A + 6B Subject to: 3A + B 3A + 3B 6 A, B 0.

13 30) A breed of cattle needs at least protein and fat units per da. Feed tpe I provides 6 protein and fat units at $/bag. Feed tpe II provides protein and fat units at $/bag. Which miture fills the needs at minimum cost? 30) Minimize + Subject to: 6 + +, 0. Minimize + Subject to: 6 + +, 0. Minimize + Subject to: 6 + +, 0. Minimize + Subject to: 6 + +, 0. TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false. Provide an appropriate response. 3) To determine the shading when graphing + 9 0, the point (0,0) would make a good test point. True or false? 3) 3) The feasible region of a set of two inequalities must alwas be unbounded. True or false? 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 33) If the inequalities 0 and 0 are included in a sstem, the feasibilit region is restricted to the aes and which quadrant? 33) Fourth Second First It is not restricted. 3

14 Answer Ke Testname: FALL 0 MTH 3 RE EX ) B ) C 3) B ) A ) A 6) A 7) B ) A 9) A ) C ) B ) D 3) D ) C ) C 6) B 7) D ) C 9) D 0) D ) C ) B 3) C ) D ) A 6) A 7) C ) C 9) D 30) C 3) FALSE 3) TRUE 33) C

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Math 132 Eam 2 Review (.1 -.5, 7.1-7.5) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the given ordered set of numbers is a solution