Linear programming applications in marketing, finance, operations management, please provide solution with linear program

Problems Note: The following problems have been designed to give you an understanding and ap- preciation of the broad range of problems that can be formulated as linear programs. You should be able to formulate a linear programming model for each of the problems. How- ever, you will need access to a linear programming computer package to develop the solu- tions and make the requested interpretations. 1. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertis- ing alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Newspaper SELF test Audience per advertisement 100,000 18,000 40,000 Cost per advertisement $2000 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not ex- ceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. a. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allo- cation of the budget among the three media, and what is the total audience reached? b. By how much would audience contact increase if an extra $100 were allocated to the promotional budget