MATH QUIZ 4 FALL’14

NAME___

Show all work to receive credit .No credit will begiven for answers only. Where possible, use at least the amount ofwork that the authors showed in the sample problems as your guide .Ifin doubt, err on the side of showing too much, .ratherthan too little, work. If you don’t work directly onthe test p1per, in the space provided under each question, you willlose two points.

The due date is 11/02/2014. Problems #1, #3 through #6, andthe comment have a 2 point value problems #2 and #7 have a 4 pointvalue. GOOD LUCK ! (:&gt) (:&gt) (:&gt)

You are on your HONOR not to get help on this quiz. It is open book,open notes, and a calculator is allowed. Submit it through theAssignment Folder, in .doc or .PDF format.

For the multiple choice questions, choose the onealternative that best completes the statement or answers thequestion, and provide work or an explanation for each one. Write theletter on the blank next to the question number.

___1.. (5-3) An optimal solution area has vertices (0, 5) (1, 1),(3, 8 ), and (9, 4). State the vertex that maximizes the objectivefunction. 2x + y.Show work.

A)(0, 5) B)(1, 1) C)(3,8) D)(9, 4)

X Y

(0, 5) 2(0) + 5 = 5

(1, 1) 2(1) + 1 = 3

(3, 8) 2(3) + 8 = 14

(9, 4) 2(9) + 4 = 22

ANS = (D) (9,4)

2-A. &amp 2-B. (5-3) A candy merchant sells two variety bags ofcandy. Each pound of variety bag A contains 60% caramels and 40%chocolates and sells for $8 a pound. Each pound of variety bag Bcontains 45% caramels and 55% chocolates .and sells for $10 a pound.The merchant has available 400 pounds of caramels and 300 pounds ofchocolates. The merchant will try to sell the amount of each brandthat maximizes her income .Let x be the number of pounds of varietybag A and y be the number of pounds of variety bag B. Make amathematical model in the form of a linear programming problem tohelp answer this question.

.40x + .55y &lt 300

.60x + .40y &lt 400

8x + 10y

___ 2-A. Since the merchant has available 300 pounds of chocolates,one inequality that must be satisfied in the situation above is:

A).40x + .55y &lt 300 B).60x + .40y &lt300 C).60x + .45y &lt 300

D).45x + .55y &lt 300E) none of theabove

A).40x + .55y &lt 300

___2-B. In the situation above, the objective function is:

A)8x + 10y B)400x + 300y C) .60 x + .40yD) .45x + .55ye) none ofthe above

A)8x + 10y

In place of work, define or explain the objective function.

The objective function is the equation that is to be optimizedsubject to other constraints, which have variables to be maximized orminimized using non-linear programming approaches. In place of work,the profit equation is the objective function while costs are theconstraints.

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__3.(7-2). Consider the following sets

U = {1, 2, 3, 4, 5, 6, 7, 8}

A = {2, 4, 6, 8}

B = {1, 2, 3, 5, 7}

A u B’ is the set

A) empty set B) set AC) {2} D) {4, 6, 8} E) none of these

NOTE: The set involved in this problem is set A union set Bcomplement (not set B).

N = 1, 2, 3, 4……8

Since B’ refers to everything that is not in set B, then

B’ = {4, 6,8}

A = {2, 4, 6, 8} all the elements in B’ are present in A

Therefore, A u B’

Must be set A

Ans: B) set A

4.. (7.2) Using the Venn diagram on page 347, determine how manyelements are in the set A∩B’

5..(7-3) A) How many 5-letter code words .are possible from the first7 letters of the alphabet if no letter is repeated?

Since repeats are not allowed:

Then

7 * 6 * 5 * 4 * 3 = 2520

B) If letters can be repeated?

Since repeats are allowed:

Then

7 * 7 * 7 * 7 * 7 = 16807

C) If adjacent letters must be different?

Since adjacent letters must be different, but the third can be thesame as the first but not the third. Same applies to the fourth andfifth.

7 * 6 * 6 * 6 * 6 = 9072

___6.(7-4).. Eight horses are entered into a race. In how many wayscan they cross the finish line, if ties are not allowed?

A) 8 to eighth powerB) 8 x 7 x 6 x 5 x 4 x 3 x 2 x1 C) 8 d) 2 to eighth power

E) none of these

The function is called 8 Factorial (8!). However, when the firsthorse crosses the finish line, there are only 7 combinations (horsesleft since there are no ties) left, then 6, then 5 until we only haveone left.

ANSB) 8 x 7 x6 x 5 x 4 x 3 x 2 x 1.

7…(7-4) A real estate company with 14 employees in their centraloffice, 8 in their north

office, and 6 in their south office is planning to lay off 12employees.

  1. How many ways can this be done?

= nCr

ANS28C12 =30,421,755

B) The company decides to lay off 5 employees from the centraloffice, 4 from the north office, and 3 from the south office. In howmany ways can this be done?

14C5 = 2002

8C4 = 70

6C3 = 20

Therefore,

ANS = 2002*70*20 = 2,802,800

8.. Please comment on this quiz in one or more complete sentences .(2points)

___9.. (7-3) EXTRA CREDIT (2 points).

At a certain university, 540 students are math and computer sciencemajors .If 300 are majoring in math, and 120 are majoring in both,how many are majoring in computer science?

NOTE: The both majors are included in the math majors, and in thecomputer science majors. This problem requires some serious thought.

A) 240 B) 420 C) 300 D) 120E) none of these