Chapter 8.2, Problem 30E

Politics A political candidate wishes to use a combination of television and radio advertisements in his campaign. Each 1-minute ad on television reaches 0.12 million eligible voters and each 1-minute ad on radio reaches 0.009 million eligible voters. The candidate believes that he must reach at least 7.56 million eligible voters and that he must buy at least 100 minutes of advertisements. If television ads cost $1000 per minute and radio ads cost $200 per minute, how many minutes of radio and television advertising does he need to minimize costs? What is the minimum cost? (See Exercise 31 in Section 8.1.)

31. Politics A political candidate wishes to use a combination of x television and y radio advertisements in his campaign. Each 1-minute ad on television reaches 0.12 million eligible voters, and each 1-minute ad on radio reaches 0.009 million eligible voters. The candidate feels that he must reach at least 7.56 million eligible voters and that he must buy at least 100 minutes of advertising.

1. a. Write the inequalities that describe these advertising requirements.
2. b. Graph the region determined by these inequalities in the context of the application.