Andrea Fontaine is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest, and she does not want the portfolio to include more than 65% stocks.
The average annual return for the stock fund she plans to invest in is 18%, whereas the average annual return for the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, whereas the most she could lose in the bond fund is 5%. To reduce her risk, she wants to limit her potential maximum losses to $100,000.
Formulate a linear programming model for this problem by defining the decision variables, objective function, and all the constraints. Do NOT solve the problem after formulating.
An advertising campaign for a new breakfast bar will be conducted in Miami area and may use TV commercials, radio commercials, and newspaper commercials. Information about the three media (for each commercial) is shown below.
Medium Cost Consumers Reached Exposure Quality
TV $2500 100000 30
Radio $ 750 25000 40
Newspaper $1500 50000 25
If the number of TV commercials cannot exceed the number of radio commercials by more than 4, and if the advertising budget is $50000, develop the model that will maximize the total number of consumers reached and achieve an exposure quality of at least 500.
Formulate a linear programming model for this problem by defining the decision variables, objective function, and all the constraints. Do NOT solve the problem after formulating.