The average daily cost
is given by
.
Find how many bicycles must be produced each day for the average cost to be no more than
.
Write the inequality related situation in the problem.
\
.
Solve the rational inequality
.



The inequality is
.
Determine the real zeros (
-intercepts of the graph )of
and the real numbers for which
is undefined.
The zeroes of the function are the values of
for which
.
THe function is 
The zeroes of
is
.
A rational function is undefined when denominator is zero.
\
is undefined for
.
Use the zeros and undefined values found in Step 1 to divide the real number line into intervals.
\Denominator of the function should not be zero.
\
The function is defined for all values of
except at
.
The function intervals are
.
Select a number in each interval, evaluate
at the number, and determine whether
is positive or negative.
If
is positive, all values of
in the interval are positive. If
is negative, all values of
in the interval are negative.
.
The real zero of numerator is
and the real zeros of denominator
.
\
So the real zeros are divide the
-axis into three intervals.
\
The function intervals are
,
, and
.
\
Choosing a number for
in each interval and evaluating
.
| Interval | \ \
| \
\
\
| \
Conclusion | \
| \
| \
\
| \
\
| \
Negative | \
| \
| \
\
| \
\
\
| \
Positive | \
| \
| \
\
| \
\
\ \ \ \ \
\ | \
Negative | \
\
\
Since
is not in the domain of
, the solution of the inequality
are in the interval notation
.
Set notation
.
Consider the solution of the inequality
.
Produce at least
bicycles.
\
Produce at least
bicycles.