Instructions

Each team  needs  to  submit  the  following  files through  Canvas  via  a  link  that  will  be  made  available  under  the Assignment link section (it is sufficient for one member of the team to submit it on behalf of the entire team):

-    An electronic copy of your spreadsheet models. The filename should be your group name and assignment name, e.g., Section_21_Team  1  Assignment_1.xlsx.

-    An electronic copy of a short typed report. In the report, you should state

A.    The mathematical formulation of your optimization model (variables, objective function, constraints), any assumptions you made (Legible, hand-written math formulation is acceptable).

a)     Provide clear definition of the decision variables

b)     Briefly state the purpose of each constraint

B.    Answers to all case questions.

-    Grading points will be allocated to the clarity and professional quality of the report.

This is a group deliverable. Work with your designated team members only.

Saving the Manatees†

"So how am I going to spend this money," thought Tom Wieboldt ashesat staring at the pictures and posters of manatees around his office. An avid environmentalist, Torn is the president of "Friends of the Manatees"- a nonprofit organization trying to help pass legislation to protect manatees.

Manatees are large, gray-brown aquatic mammals with bodies that taper to a flat, paddle-shaped tail. These gentle and slow-moving creatures grow to an average adult length of 10 feet and weigh an average of 1,000 pounds. Manatees are found in shallow, slow-moving rivers, estuaries, saltwater bays, canals, and coastal areas. In the United States, manatees are concentrated in Florida in the winter, but can be found in summer months as far west as Alabama and as far north as Virginia and the Carolinas. They have no natural enemies, but the loss of habitat is the most serious threat facing manatees today. Most human-related manatee deaths occur from collisions with motorboats.

Tom's organization has been supporting a bill before the Florida legislature to restrict the use of motorboats in areas known to be inhabited by manatees. This bill is scheduled to come up for a vote in the legislature. Tom recently received a phone call from a national environmental protection organization indicating that it will donate $300,000 to Friends of the Manatees to help increase public awareness about the plight of the manatees, and to encourage voters to urge their representatives in the state legislature to vote for this bill.

Tom intends to use this money to purchase various types of advertising media to "get the message out" during the four weeks immediately preceding the vote.

Tom  is  considering  several  different  advertising  alternatives:  newspapers,  TV,   radio,   billboards,  and magazines. A marketing consultant provided Tom with the following data on the costs and effectiveness of the various types of media being considered.

*The unit cost of $750 is a one-time cost for displaying the billboard for four weeks, not a weekly charge.

According to the markting consultant, the most effective type of advertising for this type of problem would be short TV ads during the evening prime-time hours. Thus, this type of advertising was given a "unit impact rating" of 100. The other types of advertising were then given unit impact ratings that reflect their expected effectiveness relative to an evening TV ad. For instance,a half-page magazine ad is expected to provide half the effectiveness of an evening TV ad and is therefore given an impact rating of 50.

Tom wants to allocate the $300,000 to these different advertising alternatives in a way that will maximize the impact achieved. However, he realizes that it is important to spread his message via several different advertising channels, as not everyone listens to the radio and not everyone watches TV in the evenings.

The two most widely read newspapers in the state of Florida are the Orlando Sentinel and the Miami Herald. During the four weeks before the vote, Tom wants to have half-page ads in the daily (Monday-Saturday) versions of each of these papers at least three times per week. He also wants to have one full-page ad in the daily version of each paper the week before the vote, and he is willing to run more full-page ads if this would be helpful. He also wants to run full-page ads in the Sunday editions of each paper the Sunday before the vote. Tom never wants to run a full-page and half-page ad in a paper on the same day. So the maximum number of full and half-page ads that can be run in the daily papers should be 48 (i.e., 4 weeks X 6 days per week X 2 papers = 48). Similarly, the maximum number of full and half-page ads that can be run in the Sunday papers is eight.

Tom wants to have at least one and no more than three daytime TV ads every day during the four-week period. He also wants to have at least one adon TV every night but no more than two per night.

There are 10 billboard locations throughout the state that are available for use during the four weeks before the vote. Tom definitely wants to have at least one billboard in each of the cities of Orlando, Tampa, and Miami.

Tom believes that the ability to show pictures of the cute, pudgy, lovable manatees in the print media offers a distinct advantage over radio ads. However, the radio ads are relatively inexpensive and might reach some people that the other ads will not reach. Thus, Tom wants to have at least two 15-second and at least two 30-second ads on the radio each day. However, he wants to limit the number of radio ads to five 15-second ads and five 30-second ads per day.