Finite Math 
Test #1

Oct. 9, 2000

A Track 
R. Hammack


Name: ________________________ 
Score: _________

(1) Multiply the matrices.
[ 
1

3

]  [ 
0

1

2

]  =  
7

1

5

2

5

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

+

x_{2}

≤

6 
x_{1}

+

x_{2}

≤

4 
x_{1}

≥

0  
x_{2}

≥

0 
(3)

Maximize subject to ...

P = x_{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 to solve this problem.)
(4) Use GaussJordan Elimination to solve the following system of equations:
2x_{1}

+

2x_{2}

+

x_{3}

=

9

2x_{1}

+

x_{2}

+

2x_{3}

=

11

x_{1}

+

x_{2}

+

x_{3}

=

6

(5) Use the simplex method to solve the following problem.
A hippie farmer wants to sell three crops  apples, beans, and corn  at the local Farmer's Market. He reckons it will take him 1 hour to harvest each bushel of apples, 2 hours to harvest each bushel of beans, and 1 hour to harvest each bushel of corn. Each bushel of apples weighs 20 pounds, each bushel of beans weighs 10 pounds, and each bushel of corn weighs 5 pounds. Apples sell for $15 per bushel, beans sell for $10 per bushel, and corn sells for $4 per bushel. He has a maximum of 40 hours in which to harvest the crops. Given that his aging pickup truck can haul at most 1000 pounds of produce, how many bushels of apples, beans, and corn should he take to the Farmer's Market to realize a maximum profit? (Assume he sells everything he brings to the market.)