math1324- finite math final review

MATH1324- FINITE MATH FINAL REVIEW

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

Graph the feasible region for the system of inequalities.1) 2x + y 4

x - 1 0

2) 2y + x -2y + 3x 9y 0x 0

A manufacturer of wooden chairs and tables must decidein advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities thatdescribes the manufacturer's weekly production.

3) Use x for the number of chairs and y for thenumber of tables made per week. The numberof work-hours available for construction andfinishing is fixed.

Hours per

chair

Hours per

table

Total hours

availableConstruction 1 3 27

Finishing 1 2 20

Find the value(s) of the function on the given feasibleregion.

4) Find the maximum and minimum ofz = 20x + 4y.

Use graphical methods to solve the linear programmingproblem.

5) Maximize z = 2x + 5ysubject to: 3x + 2y 6

-2x + 4y 8x 0y 0

Find the value(s) of the function, subject to the system ofinequalities.

6) Find the maximum and minimum ofP = 19x + 3y subject to:0 x 10, 0 y 5, 3x + 2y 6.

1

7) Find the minimum of P = 23x + 18y + 23 subjectto:x 0, y 0, x + y 1.

State the linear programming problem in mathematicalterms, identifying the objective function and theconstraints.

8) A car repair shop blends oil from twosuppliers.Supplier I can supply at most 49 gal with 3.8%detergent. Supplier II can supply at most 69 galwith 3.1% detergent. How much can beordered from each to get at most 100 gal of oilwith maximum detergent?

The Acme Class Ring Company designs and sells twotypes of rings: the VIP and the SST. They can produce upto 24 rings each day using up to 60 total man-hours oflabor. It takes 3 man-hours to make one VIP ring, versus 2man-hours to make one SST ring.

9) How many of each type of ring should bemade daily to maximize the company's profit,if the profit on a VIP ring is $30 and on an SSTring is $40?

Convert the constraints into linear equations by usingslack variables.

10) Maximize z = 2x1 + 8x2Subject to: x1 + 6x2 15

7x1 + 5x2 25x1 0, x2 0

Introduce slack variables as necessary and write the initialsimplex tableau for the problem.

11) Maximize z = 2x1 + 5x2subject to: 5x1 + 10x2 110

10x1 + 15x2 150x1 0, x2 0

Find the pivot in the tableau.12)

Use the indicated entry as the pivot and perform thepivoting once.

13)

Write the basic solution for the simplex tableaudetermined by setting the nonbasic variables equal to 0.

14) x1 x2 x3 x4 x5 z 3 4 0 3 1 0 18 1 5 1 7 0 0 25-3 4 0 1 0 1 19

Use the simplex method to solve the linear programmingproblem.

15) Maximize z = 3x1 + 2x2subject to: 2x1 + 3x2 4

4x1 + 2x2 12with x1 0, x2 0

A bakery makes sweet rolls and donuts. A batch of sweetrolls requires 3 lb of flour, 1 dozen eggs, and 2 lb of sugar.A batch of donuts requires 5 lb of flour, 3 dozen eggs, and2 lb of sugar. Set up an initial simplex tableau to maximizeprofit.

16) The bakery has 580 lb of flour, 660 dozen eggs,700 lb of sugar. The profit on a batch of sweetrolls is $93.00 and on a batch of donuts is $62.00.

2

Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y};B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members ofthe indicated set, using set braces.

17) A'

18) A B'

19) A' B

20) C' A'

The lists below show five agricultural crops in Alabama,Arkansas, and Louisiana.

Alabama Arkansas Louisianasoybeans (s) soybeans (s) soybeans (s) peanuts (p) rice (r) sugarcane (n)corn (c) cotton (t) rice (r)hay (h) hay (h) corn (c)wheat (w) wheat (w) cotton (t)

Let U be the smallest possible universal set that includesall of the crops listed; and let A, K, and L be the sets of fivecrops in Alabama, Arkansas, and Louisiana, respectively.Find the indicated set.

21) A K

22) K' L

23) A L

Write the sample space for the given experiment.24) An 8-sided die is rolled. (The sides contain the

numbers 1, 2, 3, 4, 5, 6, 7, and 8.)

For the experiment described, write the indicated event inset notation.

25) A die is tossed twice with the tosses recordedas an ordered pair. Represent the followingevent as a subset of the sample space: The firsttoss shows a six.

Find the probability of the given event.26) A card drawn from a well-shuffled deck of 52

cards is a red ace.

27) A card drawn from a well-shuffled deck of 52cards is an ace or a 7.

Use the given table to find the probability of the indicatedevent. Round your answer to the nearest thousandth.

28) College students were given three choices ofpizza toppings and asked to choose onefavorite. The following table shows the results.

toppings freshman sophomore junior seniorcheese 13 16 19 22

meat 19 22 16 13veggie 16 13 19 22

A randomly selected student prefers a meattopping.

Solve the problem.29) One card is selected from a deck of cards. Find

the probability of selecting a red card or aqueen.

30) A single die is rolled one time. Find theprobability of rolling an odd number or anumber less than 5.

Convert the odds that the given event will occur to theprobability that the event will occur.

31) The odds in favor of becoming the Presidentare 1 to 5,000,000.

Solve the problem.32) A survey revealed that 50% of people are

entertained by reading books, 33% areentertained by watching TV, and 17% areentertained by both books and TV. What is theprobability that a person will be entertained byeither books or TV? Express the answer as apercentage.

33) Of the coffee makers sold in an appliance store,3.0% have either a faulty switch or a defectivecord, 1.8% have a faulty switch, and 0.2% haveboth defects. What is the probability that acoffee maker will have a defective cord?Express the answer as a percentage.

34) If a single fair die is rolled, find the probabilityof a 4 given that the number rolled is odd.

35) If two cards are drawn without replacementfrom an ordinary deck, find the probabilitythat the second card is red, given that the firstcard was a heart.

3

Assume that two marbles are drawn without replacementfrom a box with 1 blue, 3 white, 2 green, and 2 redmarbles. Find the probability of the indicated result.

36) The second marble is red, given that the firstmarble is white.

Graph the linear equation.37) 5y + 10x = 15

Sketch the graph of the equation.38) y = -x2 - 2

Determine the vertex of the parabola.39) f(x) = x2 - 6x + 15

State whether the parabola opens upward or downward.40) f(x) = -6x2 + 3x + 7

Find the x- and y-intercepts. If no x-intercepts exist, stateso.

41) f(x) = 3x2 + 9x + 3

Find the rule of a quadratic function whose graph has thegiven vertex and passes through the given point.

42) vertex (5, -4); point (3, -24)

Graph the rational function.

43) f(x) = 1x - 2

Give the equation of the vertical asymptote(s) of therational function.

44) g(x) = 68x + 5

Give the equation of the horizontal asymptote of therational function.

45) f(x) = 6x + 57x - 9

Graph the function.46) f(x) = 4x

4

47) f(x) = 13

x

Solve the problem.48) An economist predicts that the buying power

B(x) of a dollar x years from now will decreaseaccording to the formula B(x) = 0.29x. Howmuch will today's dollar be worth in 2 years?Round the answer to the nearest cent.

Find the value of the expression.49) log4 64

50) log7 149

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

51) ln eA) 0 B) 1 C) e D) -1

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

Write the expression as the logarithm of a single numberor expression with a coefficient of 1. Assume all variablesrepresent positive numbers.

52) 3 ln (x + 3) - 6 ln (x2 + 7)

53) 9 log w + 7 log z - log (x - 5)

Write the expression as a sum and/or a difference oflogarithms with all variables to the first degree.

54) ln 5t9v2

55) ln 3t4v2

Evaluate the expression.56) log2 71.03

Graph the function.57) y = log5 x

58) y = ln (x + 4)

Solve the equation.59) ln (3x - 4) = ln 20 - ln (x - 5)

60) log 4x = log 5 + log (x + 3)

61) ln eln x - ln (x - 9) = ln 8

Solve the equation for s.62) log (5 + r) = log (5s - 1)

63) 4 - r = ln (6s + 8)

5

Solve the equation for c.64) log (4c - 1) = log (7 - r)

Solve the exponential equation.65) 3(10 - 2x) = 81

Solve the equation.66) 5x = 20

67) 2e4x + 1= 10

Solve the equation for c.68) 103c + 5 = d

Solve the system of two equations in two variables.69) 8x + 8y = -32

-4x - 5y = 20

Perform the indicated operation where possible.

70)-1 30 49 -4

-2 17 42 2

71) 4 4 + -27

Perform the indicated operation.

72) Let A = 1 32 4

and B = 0 4-1 6

. Find 4A + B.

Solve the problem.73) Carney and Dobler sell home and mortgage

insurance. Their sales for the months of Mayand June are given in the matrices.

Home Mortgage

M =22,000 45,000

18,000 27,000

Carney

Dobler

J =25,000 41,000

14,000 21,000

Carney

Dobler

Find the matrix that would give the change insales from May to June.

74) Barnes and Able sell life, health, and autoinsurance. Sales for May and June are given inthe matrices.

Life Health Auto

M =20,000 15,000 5000

30,000 0 17,000

Able

Barnes

J =70,000 0 30,000

20,000 25,000 32,000AbleBarnes

Find the matrix that would give total sales forthe months of May and June.

Write a matrix to display the information.75) A company makes 3 types of cable. Cable A

requires 3 black, 3 white, and 2 red wires. Brequires 1 black, 2 white, and 1 red. C requires2 black, 1 white, and 2 red. Make a 3 x 3 matrixshowing the wire requirements. Assign thecable types to the rows and the wire types tothe columns.

6

Answer KeyTestname: FINAL REVIEW MATH1324

1)

2)

3) x + 3y 27x + 2y 20 x 0 y 0

4) 220, 12

5) Maximum of 494

when x = 12

and y = 94

6) 205, 97) 418) Maximize 0.038x + 0.031y

Subject to: 0 x 490 y 69x + y 100.

9) 0 VIP and 24 SST10) x1 + 6x2 + s1 = 15

7x1 + 5x2 + s2 = 2511) x1 x2 s1 s2 z

5 10 1 0 0 11010 15 0 1 0 150-2 -5 0 0 1 0

12) 3 in row 2, column 3

7


13)

14) x1 = 0, x2 = 0, x3 = 25, x4 = 0, x5 = 18, z = 1915) Maximum is 6 when x1 = 2, x2 = 016)

x1 x2 s1 s2 s3 s4 3 5 1 0 0 0 580 1 3 0 1 0 0 660 2 2 0 0 1 0 700- 93 - 62 0 0 0 1 0

17) {r, t, v, x, z}18) {u, w}19) {q, r, s, t, v, x, y, z}20) {r, t}21) {h, s, w}22) {c, n}23) {c, h, n, p, r, s, t, w}24) {1, 2, 3, 4, 5, 6, 7, 8}25) {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

26) 126

27) 213

28) .333

29) 713

30) 56

31) 15,000,001

32) 66%33) 1.4%34) 0

35) 2551

36) 27

8


37)

38)

39) (3, 6)40) Downward

41) -3 ± 52

, 0 , (0, 3)

42) f(x) = -5(x - 5)2 - 443)

44) x = - 58

45) y = 67

9


46)

47)

48) $0.0849) 350) -251) B

52) ln (x + 3)3

(x2 + 7)6

53) log w9 · z7(x - 5)

54) 12

ln 5 + 3 ln t + ln v

55) 12

ln 3 + 2 ln t + ln v

56) 6.1504

10


57)

58)

59) 19/360) -1561) 72/7

62) 6 + r5

63) e4 - r - 86

64) 8 - r4

65) 366) 1.86167) 0.152

68) c = log d - 53

69) (0, -4)70)

-3 2-7 07 -6

71) Not defined11


72)4 167 22

73)3000 -4000

-4000 -600074)

90,000 15,000 35,00050,000 25,000 49,000

75)3 3 21 2 12 1 2

12

math1324- finite math final review

Documents