Finite Math 
Test #1

Oct. 10, 2000

F Track 
R. Hammack


Name: ________________________ 
Score: _________

(1) Perform the indicated matrix operation, or explain why it cannot be done.
(a)  [ 
5

1

][ 
1

4

] 
=


2

3

2

0

(b)  [ 
0

1

3

] 
+

[ 
0

1

2

]  =  
4

7

1

5

2

5

(2) Sketch the solutions of the following system of inequalities.
2x_{1}

+

x_{2}

≤

8 
x_{1}

+

x_{2}

≤

5 
x_{1}

+

2x_{2}

≤

8 
x_{1}

≥

0 
x_{2}

≥

0 
(3)

Maximize subject to ...

P = 10x_{1} + x_{2}

You may use any method. (However, notice that you sketched the feasible region in the previous problem. Feel free to use that information here.)
(4) Use GaussJordan elimination to solve the following system of equations:
2x_{1}

+

4x_{2}

+

2x_{4}

=

6  
x_{1}

+

2x_{2}

+

x_{3}

+

2x_{4}

=

4 
(5) Use the simplex method to solve the following problem.
A small publishing company is considering whether to publish 3 books. Let's call them book A, book B and book C. Two machines are needed to print the books, a printer and a binder. First a book is printed on the printer, then it is fed into the binder. Each copy of book A takes 6 minutes on the printer, then 4 minutes on the binder. Each copy of book B takes 4 minutes on the printer, then 2 minutes on the binder. Each copy of book C takes 2 minutes on the printer, then 1 minute on the binder. The printer is available for 1000 minutes per week, and the binder is available for 800 minutes per week. Each copy of book A will bring a profit of $2, each copy of book B will bring a profit of $1, and each copy of book C will bring a profit of $3. How many copies of each book shuld be made to realize a maximum profit?