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.
- a. Write the inequalities that describe these advertising requirements.
- b. Graph the region determined by these inequalities in the context of the application.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
MyLab Math with Pearson eText plus Worksheets for College Algebra in Context with Integrated Review -- Access Card Package (5th Edition)
- Shipping TelevisionsAn electronics discount chain has a sale on certain brand of 60-in. high-definition television set. The chain has stores in Santa Monica and El Toro and warehouses in Long Beach and Pasadena. To satisfy rush orders, 15 sets must be shipped from the warehouses to the Santa Monica store, and 19 must be shipped to the El Toro store. The cost of shipping a set is 5 from Long Beach to Santa Monica, 6 from Long Beach to El Toro, 4 from Pasadena to Santa Monica, and 5.50 from Pasadena to El Toro. If the Long Beach warehouse has 24 sets and the Pasadena warehouse has 18 sets in stock, how many sets should be shipped from each warehouse to each store to fill the orders at a minimum shipping cost?arrow_forwardAgriculture A mixture of 6 gallons of chemical A, 8 gallons of chemical B, and 13 gallons of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1,2, and 2 parts, respectively, of these chemicals. Commercial spray Y contains only Chemical C. Commercial spray Z contains A, B, and C in equal amounts. How much of each type of commercial spray is needed to get the desired mixture?arrow_forwardSales Commissions A saleswoman works at a kiosk that offers three different models of cell phones: standard with 16 GB capacity, deluxe with 32 GB capacity, and super deluxe with 64 GB capacity. For each phone that she sells, she earns a commission based on the cell phone model. One week she sells 9 standard, 11 deluxe, and 8 super-deluxe and makes $740 in commission. The next week she sells 13 standard, 15 deluxe, and 16 super-deluxe for a $1204 commission. The third week she sells 8 standard, 7 deluxe, and 14 super-deluxe, earning $828 in commission. (a) Let x, y, and z represent the commission she earns on standard, deluxe, and super-deluxe, respectively. Translate the given information into a system of equations in x, y, and z. (b) Express the system of equations you found in part (a) as a matrix equation of the form AX=B . (c) Find the inverse of the coefficient matrix A and use it to solve the matrix equation in part (b). How much commission does the saleswoman earn on each model of cell phone?arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage