Need help with this quiz. My brain is fried right now.

Need help with this quiz. My brain is fried right now. Need before 11:59 tonight

 

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MATH 106 QUIZ 4 Due: by 11:59 PM, Sunday, September 22, 2013,

(take-home part) via the Assignment Folder

NAME: _______________________________
I have completed this assignment myself, working independently and not consulting anyone except the

instructor.

INSTRUCTIONS

 The take-home part of Quiz 4 is worth 75 points. There are 10 problems (5 pages), some with multiple parts.
This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online

classroom materials, but you must work independently and may not consult anyone (and confirm this with

your submission). You may take as much time as you wish, provided you turn in your quiz no later than

Sunday, September 22, 2013.

 Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You
may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work.

Scanned work is acceptable also. In your document, be sure to include your name and the assertion of

independence of work.

 General quiz tips and instructions for submitting work are posted in the Quizzes conference.

 If you have any questions, please contact me via Private Message in WebTycho.

1. (4 pts) Determine how many six-character codes can be formed if the first, second, third, and

fourth characters are letters, the fifth character is a nonzero digit, the sixth character is an odd

digit, and repetition of letters and digits are allowed. (A digit is 0, 1, 2, .., or 9.) Show your

work . 1. __

____

A. 720

B. 175,760

C. 790,920

D. 20,563,920

2. (4 pts) Suppose that a multiple choice exam has seven questions and each question has five

choices. In how many ways can the exam be completed? Show your work. 2. ______

A. 3

5

B. 4,096

C. 16,807

D. 78,125

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3. (4 pts) Given the feasible region shown to

the right, find the values of x and y that

minimize the objective function 8x + 7y.

Show your Work. 3. _______

A. There is no minimum.

B. (x, y) = (6, 0)

C. (x, y) = (3, 2)

D. (x, y) = (1, 4)

E. (x, y) = (0, 7)

4. (4 pts) Six customers in a grocery store are lining up at the check-out. In how many different

orders can the customers line up? Show your work. 4. _______

A. 6

B. 36

C. 720

D. 46,656

5. (4 pts) A restaurant’s menu has six appetizers, four entrees, and five beverages. To order dinner, a
customer must choose one entrée and one beverage, and may choose one appetizer. (That is, a dinner

must include one entrée and one beverage, but not necessarily an appetizer. An appetizer is optional.)

How many different dinners can be ordered? Show your work. 5. _______

A. 140

B. 120

C. 2

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D. 15

HINT: There are several ways to solve the problem. Here is something to think about, in general: Declining an item

actually is a choice. For example, suppose that a person has an option of choosing a sweetener for a coffee drink.

The person might use sugar or a particular sugar-free substitute, or decline a sweetener. Declining a sweetener

means choosing no sweetener. (choices are sugar, sugar-free, or none).

6. (10 pts) Let U = {10, 20, 30, 40, 50, 60, 70, 80, 90}, A = {30, 50, 60, 90} and B = {10, 20, 50,

80, 90}.

List the elements of the indicated sets. (No work/explanation required).

(a) BA 

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(b) BA 

(Be sure to notice the complement symbol applied to A)

(c) BA 
(Be sure to notice the complement symbol applied to B)

7. (7 pts) Use the given information to complete the following table.

n(U) = 80 , n(A) = 22, n(B) = 35, n(A  B) = 15. (No work/explanation required)

A A Totals

B

B

Totals

8. (9 pts) 200 baseball fans in a Maryland county have been surveyed about the baseball teams they

watch on TV. 103 fans watch the Washington Nationals. 90 fans watch the Baltimore Orioles. 170 watch

the Washington Nationals or the Baltimore Orioles (or both).

(a) How many of the fans watch both the Washington Nationals and the Baltimore Orioles? Show work.

(b) How many of the fans watch the Baltimore Orioles but not the Washington Nationals? Show work.

(c) Complete the following Venn diagram, filling in the number of fans belonging in each of the four

regions. Circle W = {fans who watch the Washington Nationals} and Circle B = {fans who watch the
Baltimore Orioles}. (no explanation required)

U

B W

____
____

____ _____

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9. (9 pts) A panel of 7 politicians is to be chosen from a group of 15 politicians.

(a) In how many ways can the panel be chosen? Show work/explanation.

(b) Now suppose that the group of politicians consists of 5 Democrats, 7 Republicans, and 3

Independents. In how many ways can the 7-person panel be chosen if it must consist of 3 Democrats, 3

Republicans, and 1 Independent? Show some work/explanation.

10. (21 points)Two kinds of cargo, A and B, are to be shipped by a truck. Each crate of cargo A

is 25 cubic feet in volume and weighs 100 pounds, whereas each crate of cargo B is 40 cubic feet

in volume and weighs 120 pounds. The shipping company collects $180 per crate for cargo A

and $220 per crate for cargo B. The truck has a maximum load limit of 1,200 cubic feet and

4,200 pounds. The shipping company would like to earn the highest revenue possible.

(a) Fill in the chart below as appropriate.

Cargo A

(per crate)

Cargo B

(per crate)

Truck Load Limit

Volume

Weight

Revenue

Let x be the number of crates of cargo A and y the number of crates of cargo B shipped by one

truck.

(b) State an expression for the total revenue R earned from shipping x crates of cargo A and y

crates of cargo B.

(c) Using the chart in (a), state two inequalities that x and y must satisfy because of the truck’s

load limits.

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(d) State two inequalities that x and y must satisfy because they cannot be negative.

(e) State the linear programming problem which corresponds to the situation described. Be sure to
indicate whether you have a maximization problem or a minimization problem, and state the objective function

and all the inequalities. (This part is mostly a summary of the previous parts)

(f) Solve the linear programming problem. You will need to find the feasible region and

determine the corner points. You do not have to submit your graph, and you do not have to show

algebraic work in finding the corner points, but you must list the corner points of the feasible

region and the corresponding values of the objective function.

Corner Point (x, y) Value of Objective Function

(g) Write your conclusion with regard to the word problem. State how many crates of cargo A

and how many crates of cargo B should be shipped in the truck, in order to earn the highest

total revenue possible. State the value of that maximum revenue.