MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Stud Guide for Test II Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequalit. 1) ) A) B) C) D)

2 2) ) A) B) C) D) ) -2 3)

3 A) B) C) D) Graph the feasible region for the sstem of inequalities. 4) )

4 A) B) C) D)

5 ) ) - - A) B) - - C) - D) ) < -12 6)

6 A) B) C) D) Write the sstem of inequalities that describes the possible solutions to the problem. 7) 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 manufacturer's weekl production. 7) 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 A) B) C) D)

7 8) An airline with two tpes of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 70 tourist class, and 0 econom class passengers. Airplane P1 can accommodate 20 first class, 0 tourist class, and 1 econom class passengers. Airplane P2 can accommodate 18 first class, 30 tourist class, and 44 econom class passengers. Let represent the number of planes of tpe P1 and represent the number of planes of tpe P2. A) , 0 C) , 0 B) , 0 D) z z 70 0, 0 8) Graph the feasible region of the sstem. 9) An airline with two tpes of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 70 tourist class, and 0 econom class passengers. Airplane P1 can accommodate 20 first class, 0 tourist class, and 1 econom class passengers. Airplane P2 can accommodate 18 first class, 30 tourist class, and 44 econom class passengers. Let represent the number of planes of tpe P1 and represent the number of planes of tpe P2. 9) A) B)

8 C) D) Use the indicated region of feasible solutions to find the maimum and minimum values of the given objective function. ) z = ) (0, ) (, ) (0, 3) (2, 0) (, 0) A) Maimum of 1; minimum of 9 B) Maimum of 1; minimum of 9 C)Maimum of 12; minimum of 9 D) Maimum of 12; minimum of 1 8

9 Use graphical methods to solve the linear programming problem. 11) Minimize z = subject to: ) - - A) Minimum of 1.08 when = 4 and = 3 B) Minimum of 1.2 when = 4 and = 4 C)Minimum of 1.86 when = 9 and = 2 D) Minimum of 1.02 when = 3 and = 4 12) Minimize z = subject to: ) - - A) Minimum of 20 when = 2 and = 4 B) Minimum of 0 when = 0 and = 0 C)Minimum of 20 when = 2 and = 4, as well as when = and = 0, and all points in between D) Minimum of 20 when = and = 0 9

10 Solve the problem. 13) The Acme Class Ring Compan designs and sells two tpes of rings: the VIP and the SST. The can produce up to 24 rings each da using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How man of each tpe of ring should be made dail to maimize the compan's profit, if the profit on a VIP ring is $30 and on an SST ring is $40? A) 16 VIP and 8 SST B) 12 VIP and 12 SST C)8 VIP and 16 SST D) 0 VIP and 24 SST 13) Use slack variables to convert the constraints into linear equations. 14) Maimize z = Subject to: with: 1 0, 2 0 A) s1 = s1 = 47 C) = s = s B) s1 = s2 = 47 D) s s ) Solve the problem. 1) An airline with two tpes of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 70 tourist class, and 0 econom class passengers. For a certain trip, airplane P1 costs $,000 to operate and can accommodate 20 first class, 0 tourist class, and 1 econom class passengers. Airplane P2 costs $800 to operate and can accommodate 18 first class, 30 tourist class, and 44 econom class passengers. How man of each tpe of airplane should be used in order to minimize the operating cost? A) 11 P1 planes and 7 P2 planes B) 7 P1 planes and 11 P2 planes C) P1 planes and 17 P2 planes D) 9 P1 planes and 13 P2 planes 1) Epress the given situation as a linear inequalit. 16) Product A requires 4 hr on machine M, while product B needs 3 hr on the same machine. The machine is available for at most 48 hr per week. Let be the number of product A made and be the number of product B. A) B) 7( + ) 48 C)48( + ) 7 D) ) Solve the problem. 17) Zach is planning to invest up to $4,000 in corporate and municipal bonds. The least he will invest in corporate bonds is $8000 and he does not want to invest more than $28,000 in corporate bonds. He also does not want to invest more than $28,311 in municipal bonds. The interest is 8.2% on corporate bonds and.9% on municipal bonds. This is simple interest for one ear. What is the maimum value of his investment after one ear? A) $20,299 B) $31,299 C) $12,293 D) $48,299 17)

11 Introduce slack variables as necessar, and write the initial simple tableau for the problem. 18) Find 1 0 and 2 0 such that and z = is maimized. 18) A) 1 2 s1 s2 z C) 1 2 s1 s2 z B) 1 2 s1 s2 z D) 1 2 s1 s2 z ) Find 1 0 and 2 0 such that and z = is maimized. 19) A) 1 2 s1 s2 z C) 1 2 s1 s2 z B) 1 2 s1 s2 z D) 1 2 s1 s2 z Write the solutions that can be read from the simple tableau. 20) s1 s2 z A) 1, 2, s1 = 0, 3 = 14, s2 = 2, z = 18 B) 1, 2, s1 = 0, 3 = 2, s2 = 14, z = 18 C)1, 2, s1 = 0, 1 = 2, s2 = 14, z = 18 D) 1, 2, s1 = 0, = 2, s2 = 14, z = 18 20) 21) 1 2 s1 s2 s3 z A) s3 = 8, s1 = 16, 1 = 2, z = 13; 2, s2 = 0 B) s2 = 8, s1 = 16, 1 = 2, z = 13; 2, s3 = 0 C)s2 = 8, s3 = 16, 1 = 2, z = 13; 2, s1 = 0 D) s2 = 8, s1 = 16, s3 = 2, z = 13; 1, 2 = 0 21) 11

12 Pivot once about the circled element in the simple tableau, and read the solution from the result. 22) 22) A) 2 = 3, 1 = -2, z = ; 3, s1, s2 = 0 B) 2 = 3, 1 = -2, z = 6; 3, s1, s2 = 0 C)2 = 3, 1 = 2, z = 6; 3, s1, s2 = 0 D) 2 = 6, 1 = 22, z = 6; 3, s1, s2 = 0 A baker makes sweet rolls and donuts. A batch of sweet rolls requires 3 lb of flour, 1 dozen eggs, and 2 lb of sugar. A batch of donuts requires lb of flour, 3 dozen eggs, and 2 lb of sugar. Set up an initial simple tableau to maimize profit. 23) The baker has 780 lb of flour, 600 dozen eggs, 660 lb of sugar. The profit on a batch of sweet rolls 23) is $90.00 and on a batch of donuts is $8.00. A) s d p C) s d p B) s d p D) s d p ) The baker has 320 lb of flour, 340 dozen eggs, 300 lb of sugar. The profit on a batch of sweet rolls is $8.00 and on a batch of donuts is $ ) A) s d p C) s d p B) s d p D) s d p

13 The initial tableau of a linear programming problem is given. Use the simple method to solve the problem. 2) s1 s2 z A) Maimum at 36 for 2 = 2, s1 = 8 B) Maimum at 32 for 2 = 8, s1 = 2 C)Maimum at 18 for 2 = 8, 3 = 2 D) Maimum at 9 for 1 = 8, 2 = 2 2) Use the simple method to solve the linear programming problem. 26) Maimize z = subject to: with 1 0, 2 0 A) Maimum is 14.6 when 1 = 2., 2 = 2.3 B) Maimum is 12 when 1 = 6, 2 = 0 C)Maimum is 6 when 1 = 14, 2 = 0 D) Maimum is 24 when 1 = 6, 2 = 0 26) A manufacturing compan wants to maimize profits on products A, B, and C. The profit margin is $3 for A, $6 for B, and $1 for C. The production requirements and departmental capacities are as follows: Department Production requirement Departmental capacit b product (hours) (Total hours) Assembling Painting Finishing A B C ,000 38,000 28,000 27) What are the coefficients of the objective function? 27) A) 2, 3, 2 B) 3, 6, 1 C)2, 3, 1 D) 1, 2, 2 Use the simple method to solve the linear programming problem. 28) Maimize z = subject to: with 1 0, 2 0 A) Maimum is 17 when 1 = 1, 2 = 1 B) Maimum is 4 when 1 =, 2 = 0 C)Maimum is 18 when 1 = 2, 2 = 0 D) Maimum is 16 when 1 = 0, 2 = 2 28) A manufacturing compan wants to maimize profits on products A, B, and C. The profit margin is $3 for A, $6 for B, and $1 for C. The production requirements and departmental capacities are as follows: Department Production requirement Departmental capacit b product (hours) (Total hours) Assembling Painting Finishing A B C ,000 38,000 28,000 29) What is the constraint for the painting department? 29) A) A + 2B + 2C 38,000 B) 2A + 3B + C 28,000 C)2A + 3B + 2C 30,000 D) A + 2B + 2C 38,000 13

14 State the dual problem. Use 1, 2, 3 and 4 as the variables. Given: 1 0, 2 0, 3 0, and ) Maimize z = subject to: , 2 0 A) Minimize w = subject to: C)Minimize w = subject to: B) Minimize w = subject to: D) Minimize w = subject to: ) Find the transpose of the matri. 31) A) B) C) D) ) The initial tableau of a linear programming problem is given. Use the simple method to solve the problem. 32) s1 s2 s3 z A) Maimum at 24 for 2 = 4, s2 = 1, s3 = 4 B) Maimum at 36 for 2 = 4, 3 = 2, s2 = 4 C)Maimum at 8 for 2 = 6, s2 = 2, s3 = 8 D) Maimum at 30 for 2 = 3, s3 = 4 32) 14

15 State the dual problem. Use 1, 2, 3 and 4 as the variables. Given: 1 0, 2 0, 3 0, and ) Minimize w = subject to: , 2 0, 3 0, 4 0 A) Maimize z = subject to: C)Maimize z = subject to: B) Maimize z = subject to: D) Maimize z = subject to: ) Use the simple method to solve the linear programming problem. 34) Minimize w = subject to: , 2 0 A) 30. when 1 = 4. and 2 = 0 B) 31. when 1 = 1 and 2 = 2 C)4 when 1 = 24 and 2 = 1 D) 48 when 1 = 0 and 2 = 24 34) A to making compan has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim. 3) It costs the compan $1.81 to make each dog and $1.17 for each dinosaur. What is the compan's 3) minimum cost? A) $17. B) $39 C) $298 D) $317 Find the maturit value and the amount of simple interest earned. Round to the nearest cent. 36) $8397 at 3.9% for 4 months A) $806.16; $9.16 B) $ ; $81.87 C) $833.4; $136.4 D) $807.08; $ ) Solve the problem. 37) If $300 earned simple interest of $13.13 in 7 months, what was the simple interest rate? A) 6.% B) 8.% C) 7.% D) 9.% 37) Find the compound amount for the deposit. Round to the nearest cent. 38) $1,000 at 6% compounded semiannuall for 6 ears A) $17,9.78 B) $20, C) $21, D) $21, ) Find the interest rate for each deposit and compound amount. 39) $9700 accumulating to $12,891.44, compounded monthl for 6 ears. A) 4.7% B) 4.9% C) 4.% D) 4% 39) 1

16 Find the amount that should be invested now to accumulate the following amount, if the mone is compounded as indicated. 40) $7700 at 6% compounded annuall for 2 ears. 40) A) $ B) $ C) $ D) $ Find the effective rate corresponding to the given nominal rate. Round to the nearest hundredth. 41) 6% compounded semiannuall A) 6.00% B) 6.17% C) 6.14% D) 6.09% 41) Pivot once about the circled element in the simple tableau, and read the solution from the result. 42) 42) A) 1 = 12, s1 = 6, z = 12; 2, 3, s2 = 0 B) 1 = 12, s1 = 42, z = 12; 2, 3, s2 = 0 C)1 = 6, s1 = -6, z = 6; 2, 3, s2 = 0 D) 1 = 12, s1 = -6, z = 12; 2, 3, s2 = 0 Use slack variables to convert the constraints into linear equations. 43) Maimize z = subject to: with: 1 0, 2 0, 3 0 A) = s = s2 + 0 C) s1 = s2 = 0 B) = s = s2-0 D) s1 = s1 = 0 43) Solve the problem. 44) June made an initial deposit of $0 in an account for her son. Assuming an interest rate of 4% compounded quarterl, how much will the account be worth in ears? A) $ B) $ C) $ D) $ ) Find the sum of the first five terms of the geometric sequence. 4) a = 3, r = 3 A) 33 B) 360 C)361 D) 363 4) Solve the problem. 46) Barbara knows that she will need to bu a new car in 3 ears. The car will cost $1,000 b then. How much should she invest now at %, compounded quarterl, so that she will have enough to bu a new car? A) $13, B) $12, C) $12,340.4 D) $13, ) Find the future value of the ordinar annuit. Interest is compounded annuall, unless otherwise indicated. 47) R = $0, i = 0.06, n = 9 A) $26.64 B) $989.7 C) $ D) $ ) 16

17 Find the amount of each pament to be made into a sinking fund so that enough will be present to accumulate the following amount. Paments are made at the end of each period. The interest rate given is per period. 48) $8900; mone earns 7% compounded annuall; 1 annual paments 48) A) $ B) $22.80 C) $ D) $34.17 Solve the problem. Round to the nearest cent. 49) If Bob deposits $000 at the end of each ear for 2 ears in an account paing 6% interest compounded annuall, find the final amount he will have on deposit. A) $ B) $1, C) $, D) $ ) Epress the given situation as a linear inequalit. 0) Phil Leitz needs at least 3 units of a nutritional supplement per da. Red pills provide units and blue pills provide 7. Let be the number of red pills and be the number of blue pills. A) 12( + ) 3 B) 3( + ) 12 C) D) + 3 0) 17

18 Answer Ke Testname: TESTII 1) B 2) A 3) B 4) C ) B 6) A 7) B 8) C 9) A ) C 11) D 12) C 13) D 14) B 1) D 16) A 17) D 18) C 19) B 20) B 21) B 22) B 23) B 24) C 2) B 26) D 27) B 28) C 29) A 30) B 31) A 32) A 33) A 34) D 3) C 36) A 37) C 38) D 39) A 40) A 41) D 42) D 43) C 44) D 4) D 46) B 47) C 48) D 49) C 0) C 18