“So how am I going to spend this money,” thought Tom Wieboldt as he sat staring at the pictures and posters of manatees around his office. An avid environmentalist, Tom 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 they 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 loss of habitat is the most serious threat facing manatees today. Most human-related manatee deaths occur from collisions with motor boats.

Tom’s organization has been supporting a bill before the Florida legislature to restrict the use of motor boats 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 they are going to 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.

            

Advertising Medium	unit Cost	unit impact rating
Half-page, daily paper	$800	55
Full-page, daily paper	$1,400	75
Half-page, Sunday paper	$1,200	65
Full-page, Sunday paper	$1,800	80
Daytime TV spot	$2,500	85
Evening TV spot	$3,500	100
Highway billboards	$750	35
15-second radio spot	$150	45
30-second radio spot	$300	55
Half-page, magazine	$500	50
Full-page, magazine	$900	60

According to the marketing 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 it is important to spread his message via several different advertising channels because 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 prior to 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-page ads and half-page ads that can be run in the daily papers should be 48 (that is, 4 weeks × 6 days per week × 2 papers = 48). Similarly, the maximum number of full-page ads and half-page ads that can be run in the Sunday papers is 8.

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 ad on 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 1 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 may reach some people that the other ads will not reach. Thus, Tom wants to have at least two 15-second ads 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.

There are three different weekly magazines in which Tom can run ads. Tom wants to run full-page ads in each of the magazines at some point during the four-week period. However, he never wants to run full-page ads and half-page ads in the same magazine in a given week. Thus, the total number of full-page and half-page magazine ads selected should not exceed 12 (that is, 4 weeks × 3 magazines × 1 ad per magazine per week = 12 ads).

Although Tom has some ideas about the minimum and maximum number of ads to run in the various types of media, he’s not sure how much money this will take. And if he can afford to meet all the minimums, he’s really confused about the best way to spend the remaining funds. So again Tom asks himself, “How am I going to spend this money?”

1. Create a spreadsheet model for this problem and solve it. What is the optimal solution?

2. Of the constraints Tom placed on this problem, which are “binding” or preventing the objective function from being improved further?

3. Suppose Tom was willing to increase the allowable number of evening TV ads. How much would this improve the solution?

4. Suppose Tom was willing to double the allowable number of radio ads aired each day. How much would this improve the solution?