Math 140
Test Four
name (10 points)
This entertaining fifty-minute test covers sections 5.1-2, 4-6 and 6.1-4 of Blitzer’s College Algebra: An
Early Function Approach. Clearly indicate your answers. Unless otherwise indicated, all parts of
all problems are five points each.
1. Solve the following system of equations and use set notation to express their solution sets.
a. 2x = 3y + 4
4x – 6y = 6
b.
x + 3y = 6
3x + 9y = 24
2. Solve the following systems
a. xy = 
2
2
x + y = 
b. x – y = 1
2
y = x +1
(6 points each)
3. Write the augmented matrix for the following system of equations
8x + 2y – 8z = 7
7x  5y + 2z = 7
9x  3y + 4z = 

4. Write the system of equations represented by the augmented matrix. Use x, y, and z for the
variables.
2 0 4 | 2
4 5 3 | 3


8 0 1 | 0
5. Solve the following systems of equations.
a. x
– 3z = 2
2x  y + 2z = 2
x y  5z = 
b. 3x + 2y – 3z = 2
2x  5y + 2z = 2
(6 points each)
6. Solve the following systems of equations.
(6 points)
3x + 2y – 3z = 2
2x  5y + 2z = 2
4x  3y + 4z = 
7 4 0
7. Let A =  0 3 1 ,
1 1 
1 2 1
B =  0 1 1 , and C =  2 0  . Perform the indicate operations.
 1 1
a. A + 3B
b. CA
c. AC
8.
 2
Find the inverse of the matrix  1
 2
4 4 
2 4 .
4 3 
Model A
Model B
Total
8
hours/bike
3
hours/bike
200
hours
Assembling
mountain bicycles. The times in hours
Painting 7 hours/bike 4 hours/bike 108 hours
required for assembling and painting are
$25
$15
maximize
Profit
given in the table. We desire to
maximize the profit. Write the objective function and constraints below. Do not graph or solve.
9. A manufacturer produces two models of
a. Objective Function:
(3 points)
b. Constraints:
(8 points)
10.Graph the system of inequalities
representing the following system of
constraints. Label each vertex with the
coordinates for the point. (8 points)
Constraints:
x > 0, y > 0
2x + y < 8
x+y>4
11.For the set of constraints in the previous problem, determine the maximum of the following
objective function and the values of x and y for which it occurs.
Objective function: z = 2x  3y
Minimum is _____ at x = ____ and y = _____
Maximum is _____ at x = ____ and y = _____
(6 points)