Answers to Sample Test!
 
 
1)  a)  7x > 24
            x > 24/7
         o------------->
        24/7
 
     b)  Multiply both sides by 12 to get
                     8 - 4x < 9 - 6x
                     2x + 8 < 9
                     2x < 1
                        x < 1//2
 
          <-----------]   closed dot!
                        1/2
 
 
     c)  x < -5 or x > 5
 
      <----------]              [------------->
                   -5             5
 
 
     d)  -7 < x - 5 < 7
          -2 < x < 12
 
            o---------------o
           -2                 12
 
 
     e)  -23 < 5 - 2x < 23
          -28 < -2x < 18
           14 > x > -9
 
              [-------------------------]
              -9                             14
 
 
     f)  3 < x - 2 < 7 or -3 > x - 2 > -7
          5 < x < 9 or -1 > x > -5
 
             [---------]               [-------------]
            -5         -1              5               9
 


2)   a)  (x - 1)(x - 4) > 0
 
                 -               -                 +          (x - 4)
                 -               +                +          (x - 1)
         <-----------0-----------0------------->
                        1              4
  We want positive.  Answer:
         <-----------0              0------------>
                         1              4
 
 
     b)  (x2 - 1)(x2 + 1) < 0
           (x - 1)(x + 1)(x2 + 1) < 0
 
                    +             +                  +             (x2 + 1)
                    -              -                   +             (x - 1)
                    -              +                  +              (x + 1)
             <---------0------------0-------------------------->
                         -1              1
    We want negative.  The answer is:
 
                         0--------------0
                        -1                 1
 
     c)                   -                   +              +                  +         (x + 3)
                           -                   -               +                  +         (x - 4)
                           -                   -               -                   +          (x - 5)
                  <---------------[]-------------[]-----------0--------------->
                                      -3               4            5
     We want negative:  Answer
 
                  <----------------]                [-----------0
                                       -3              4             5
     d)
The zeros are at -2.6, .8 and 1.7
We want the area to be < 0.  We need all areas of the above graph that are beneath the x-axis.
Answer:
<---------------0           0-----0
                                                                         -2.6         .8     1.7
 
 
e)
 
The zeros are -1, and .5
We want the area above the x-axis
 
                                                                  0-------------------->
                                                                  .5

3)  a)
 
b)
 
c)
The area is from -2 to 1 and 5 to 8 exclusive.  The lines are dotted!

4)  a)
 
b)
 
c)

5)
The corner points are:  (0, 0), (0, 2), (2, 1) and (3, 0)
P = 2x + 3y
(0, 0) yields 0
(0, 2) yields 6
(2, 1) yields 7
(3, 0) yields 6
The maximum value is 7 and it happens at (2, 1)

6)
x = amount of corn
y = amount of wheat
constraints
x > 0
y > 0
x + y > 27
x > 2y
 
objective function:  C = 250 x + 350y
The corner points are (18, 9) and (27, 0)
(18, 9) yields 7650
(27, 0) yields 6750
To minimize, take (27, 0)