Write each inequality or compound inequality using interval notation.See Sections 1.1 and 2.6.
53.xÚ 0 54.x... 0 55.x 61 or x 71 56.- 4 ...x... 4PREVIEW EXERCISES
3.5 Introduction to Relations and Functions
EXERCISES 47– 52FOR INDIVIDUAL OR GROUP WORK
Suppose a factory can haveno more than 200 workers on a
shift, but must haveat least 100 and must manufactureat least
3000 units at minimum cost. The managers need to know how
many workers should be on a shift in order to produce the
required units at minimal cost. Linear programmingis a
method for finding the optimal (best possible) solution that
meets all the conditions for such problems.
Let x represent the number of workers and y represent
the number of units manufactured. Work Exercises 47– 52
in order.
47.Write three inequalities expressing the conditions
given in the problem.
48.Graph the inequalities from Exercise 47and shade the intersection.
49.The cost per worker is $50 per day and the cost to manufacture 1 unit is $100. Write
an equation in x, y, and Crepresenting the total daily cost C.
50.Find values of xand yfor several points in or on the boundary of the shaded region.
Include any “corner points.” These are the points that maximize or minimize C.
51.Of the values of xand ythat you chose in Exercise 50,which gives the least value
when substituted in the cost equation from Exercise 49?
52.What does your answer in Exercise 51mean in terms of the given problem?RELATING CONCEPTS
OBJECTIVES
Introduction to Relations and Functions
3.5
1 Distinguish between
independent and
dependent
variables.
2 Define and identify
relations and
functions.
3 Find the domain
and range.
4 Identify functions
defined by graphs
and equations.
OBJECTIVE 1 Distinguish between independent and dependent variables.
We often describe one quantity in terms of another. Consider the following:
- The amount of a paycheck for an hourly employee depends on the number of hours
worked.
- The cost at a gas station depends on the number of gallons of gas pumped.
- The distance traveled by a car moving at a constant rate depends on the time traveled.
We can use ordered pairs to represent these corresponding quantities. We indicate the
relationship between hours worked and paycheck amount as follows.
Working 5 hr results in a $ 40 paycheck.Number of Paycheck amount
hours worked in dollars