An advertising agency buys local radio and TV slots for its clients and wants to maximize the total audience exposure for all clients. Its client has a maximum budget of $1 million per month. Each radio slot reaches 1000 customers and each TV slot reaches 3000 different customers. Radio slots cost $400, provided at least 100 slots are taken in any month, and TV slots cost $20000 with no restrictions on the number of slots. Each radio slot requires 20 hours and each TV slot requires 50 hours of the agency's executive time out of a total of 4000 hours available each month.
1. Formulate the above problem as a LP problem.
2. Can the above problem be solved graphically? Why or why not?
3. Use QM to solve the above LP problem.
4. Use QM to discuss the existence of multiple optimal solutions.