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

 2x1 + x2 ≤ 8 x1 + x2 ≤ 5 x1 + 2x2 ≤ 8 x1 ≥ 0
 x2 ≥ 0

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?