The United Broadcast Network (UBN) sells to advertisers commercial advertising slots on its television shows. The network announces its new fall television schedule during the previous spring and shortly thereafter begins selling its inventory of advertising slots to its customers. Long-standing priority customers receive the first opportunities to purchase advertising slots. The new fall season begins in the third week of September. Advertising slots are mostly 15 seconds and 30 seconds in duration. The network develops a detailed sales plan for the year, typically on a monthly, bimonthly, 6-week, or quarterly basis. Advertisers generally have certain shows in mind that they prefer to advertise on in order to reach a certain demographic audience that they want to market their product to, as well as a specific advertising budget. The network sells advertising slots at rates based on a performance score related to the popularity of a show, primarily determined by demographics and audience size.

Nanocom, a business software development firm, wants to purchase 30- and 15-second advertising slots on several shows this coming fall. Nanocom wants to reach an older, more mature, upper-income audience that is likely to include many high-tech businesspeople. It has an advertising budget of $600,000, and it has informed the UBN advertising staff that it prefers to purchase ads on the following shows: Bayside, Newsline, The Hour, Cops and Lawyers, The Judge, Friday Night Football, and ER Doctor. Newsline and The Hour are news magazine shows, whereas the others are adult dramas, except for Friday Night Football, which is professional football. Nanocom wants at least 50% of the total number of advertising slots it purchases to be on Newsline, The Hour, and Friday Night Football. Nanocom would like UBN to develop a sales plan covering the 6-week period beginning with the third week in October through November (including the November sweeps).

As indicated, UBN bases its sales plans on performance scores for the different shows. The primary objective of both UBN and the advertiser is to develop a sales plan that will achieve the highest total performance score. The performance scores are based on several factors, including how well the show matches the desired audience demographics, the audience strength of the show, the historical ratings for the time slot, the competing shows in the same time slot, and the performance of adjacent shows. The network sets its advertising rates based on these performance scores. Both the performance scores and the rates are then multiplied by a weighting factor that is based on the week of the show and, because total viewers vary according to the week of the year, the total audience expected during that week. The following table shows the costs, performance scores, and available inventory of advertising slots for 15- and 30-second commercials for each show:

               

Show	Commercial Length (seconds)	Cost ($1,000s)	Performance Score	Available Inventory
Bayside	30	$50.0	115.2	3
	15	25.0	72.0	3
Newsline	30	41.0	160.0	4
	15	20.5	100.0	1
The Hour	30	36.0	57.6	3
	15	18.0	36.0	3
Cops and Lawyers	30	45.0	136.0	4
	15	27.5	85.0	2
The Judge	30	52.0	100.8	2
	15	26.0	63.0	2
Friday Night Football	30	25.0	60.8	4
	15	12.5	38.0	2
ER Doctor	30	46.0	129.6	3
	15	23.0	81.0	1

The network advises, and Nanocom agrees, that there should be a minimum and maximum number of advertising slots during each of the 6 weeks and that Nanocom should have at most only one ad slot (either 15 or 30 seconds) per show per week. The following table shows the weighting factor each week and the minimum and maximum numbers of slots per week:

     

	October		November
Week	3	4	1	2	3	4
Weight	1.1	1.2	1.2	1.4	1.4	1.6
Minimum	1	1	2	2	2	3
Maximum	4	5	5	5	5	5

Assist UBN in developing a sales plan for the 6-week period to maximize the total performance score for Nanocom.