Suppose your theater group is putting on a play. You are responsible for publicity. You have $10,000 to spend on radio and television time for advertising the play to the public. Every 30-second radio commercial costs $50, while 40 seconds of television time on a local channel costs $400. You know that you want at least 20 radio commercials, but no more than 40 radio announcements in total. You would also like to have at least 10 40-second television commercials. In this project, you will use systems of linear equations and inequalities to determine how much radio and television time you should schedule so that the play gets the most amount of exposure within your budget.

Write the expression for using each of the following.

1.  Radio commercial time   _____________________________________________________

2.  Television commercial time   __________________________________________________

3.  Total commercial time    _____________________________________________________

Write the inequalities that satisfy the constraints of the problem.

4.  At least 20 radio commercials but no more than 40.      _______________________________________________________________________

5.  At least 10 television commercials.      _______________________________________________________________________

6.  Radio commercials cost $50 for one time period and television commercials cost $400 for one      time period and you can spend no more than $10,000.      _______________________________________________________________________

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Career Connection to Teaching with Technology