Math Quiz

See attached

NAME:_______________________________

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

· The quiz is worth 100 points. There are 8 problems. 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, February 10.
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 by e-mail or phone (540-338-7120).

1. (7 pts) The matrix below is the final matrix for a system of two linear equations in the variables x1, and x2. What can be concluded about the solution of the system? (no explanation required)

1. _______

A. There is no solution.

B. The unique solution to the system is x1 = 5 and x2 = 2.

C. There are infinitely many solutions. The solution is x1 = 5t 2 and x2 = t, for any real number t.

D. There are infinitely many solutions. The solution is x1 = 5t 2 and x2 = t, for any real number t.

2. (8 pts) The
shaded (purple) portion of the graph is the solution set of which inequality? 2. ___

Show work or explain how you have made your choice.

A. y −2x + 6
B. y −x  6
C. y 2x + 6
D. y 2x  6

3. (8 pts) Which of the following points is in the feasible region of the system 3. _______

of inequalities? That is, which of the following points satisfies all three inequalities below?

y 

3x + y 

x + y 

Show work or explain how you have made your choice.

A. (1, 9)

B. (2, 7)

C. (3, 2)

D. (9, 1)

4. (8 pts) State the result of performing the row operation ( 5)R2 + R1 R1 on the matrix

Note that you are not asked to solve the system. Instead you are asked to perform a particular row operation.

5. (11 pts) Given the following application, define two variables, express your answer to the question as a linear inequality, and also state appropriate nonnegative restrictions. (You are not asked to produce a graph.)

Tess wants to purchase sliced ham and turkey from the deli for a lunch gathering. Ham costs $6.99 per pound and turkey costs $5.50 per pound. How many pounds of each type of meat can Tess purchase if she can spend at most $25 altogether?

Template for problems involving augmented matrix methods: (If you wish, for problems #6 and #7 , you can use the Equation Editor template shown above, to make the typing easier. Just copy, paste where appropriate, and edit with the Equation Editor as needed. Or, you are welcome to use a table or a spreadsheet, or to hand-write and scan.)

6. (17 pts) Solve the system by using augmented matrix methods. Show your steps (row operations) in a similar way to the examples in the book in section 4.2.

2x + 2y = 4

3x + 5y = 

7. (17 pts) Solve the system by using augmented matrix methods. Show your steps (row operations) in a similar way to the examples in the book in section 4.2.

4x 8y = 

5x + 10y = 

8. (24 pts) Consider the following graph of a feasible region, which is bounded by the lines

3x + y = 5, –3x + y = 3, x = 0, and y = 0, as indicated.

(a) Write the system of inequalities corresponding to the graph of the feasible region.

(For each , replace by either or , as appropriate.)

3x + y 5

–3x + y 3

x 0

y 0

(b) Find the coordinates of the corner points A, B, C, and D of the feasible region.

For each of the four corner points, state which system of equations must be solved, and show how to solve it. (Continue on another page for more space.)