| 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.
|
2x1
|
+
|
x2
|
≤
|
8 |
|
x1
|
+
|
x2
|
≤
|
5 |
|
x1
|
+
|
2x2
|
≤
|
8 |
|
x1
|
≥
|
0 |
|
x2
|
≥
|
0 |
|
(3)
|
Maximize subject to ...
|
P = 10x1 + x2
|
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 Gauss-Jordan elimination to solve the following system of equations:
|
2x1
|
+
|
4x2
|
+
|
2x4
|
=
|
6 | ||
|
x1
|
+
|
2x2
|
+
|
x3
|
+
|
2x4
|
=
|
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?