For this discussion topic each student is required to have at least 2 postings: One answering at least one of the questions and a second responding to another student’s posting. Please select a question that has not been answered by the time you post your response. You can select any question to answer once all questions are answered. Please do not copy another student’s posting.

This discussion will close at midnight Sunday, October 21^{st}.

1. A hospital dietitian prepares breakfast menus every morning for the hospital patients. Part of the dietitian’s responsibility is to make sure that minimum daily requirements for vitamins A and B are met. At the same time, the cost of the menus must be kept as low as possible. The main breakfast staples providing vitamins A and B are eggs, bacon, and cereal. The vitamin requirements and vitamin contributions for each staple follow:

Vitamin Contributions Minimum Daily

Vitamin mg/Egg mg/Bacon Strip mg/Cereal Cup Requirements

A 2 4 1 16

B 3 2 1 12

An egg costs $0.04, a bacon strip costs $0.03, and a cup of cereal costs $0.02. The dietitian wants to know how much of each staple to serve per order to meet the minimum daily vitamin requirements while minimizing total cost.

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.

2. The Pyrotec Company produces three electrical products—clocks, radios, and toasters. These products have the following resource requirements:

Resource Requirements

Cost/Unit Labor Hours/Unit

Clock $ 7 2

Radio 10 3

Toaster 5 2

The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12. The company wants to know the optimal product mix that will maximize profit.

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.

3. Janet Lopez 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.

4. An advertising campaign for a new breakfast bar will be conducted in Baltimore 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.

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