The situation. Advertising firm Night & Day, Inc. (NDI) has been hired to conduct an ad campaign for a client. After considering all the possible advertising media and the target market, NDI has limited next months ads to 5 sources (listed in the table below), each of which reaches a different number of potential customers, costs a certain amount, and has its own exposure quality.

The situation. Advertising firm Night & Day, Inc. (NDI) has been hired to conduct an ad campaign for a client. After considering all the possible advertising media and the target market, NDI has limited next month's ads to 5 sources (listed in the table below), each of which reaches a different number of potential customers, costs a certain amount, and has its own "exposure quality." Exposure quality units measure the relative value of one ad in each source and take into account factors such as audience demographics, image presented, and ad quality Potential Customers Cost per Maximum Times Advertising Source Daytime TV Exposure Ad (S)Available per Month Quality Units 1,500 Reached per Ad 1,000 2,000 1,500 2,500 15 65 (1-min. commercial) Evening TV 3,000 10 90 (30-sec. commercial) Daily Newspaper 400 25 40 (full page ad) Sunday Newspaper 1,000 60 (1/2 page color) Radio 300 100 30 20 (30 second spot) NDI's goal is to maximize the total exposure quality from the ad campaign. The client has given NDI an advertising budget of $30,000 - see constraint [1] - and has imposed several restrictions on its use. Specifically, at least 10 TV commercials must be used, but no more than $18,000 may be spent on these commercials - see constraints [2-3]. Also, the client wants at least 50,000 potential customers to be reached through all sources - see constraint [4]. Finally, the fourth column of the table above gives limits on the number of times each advertising source may be used in a month - see constraints [5-9] LP Formulation: NDI has 5 decisions to make: . DT number of Daytime TV ads to run . ET number of Evening TV ads to run . DN number of Daily Newspaper ads to run SN number of Sunday Newspaper ads to run RAnumber of Radio Ads to run Maximize 65DT + 90ET 40DN60SN 20RA subject to: 1,500DT3,000ET 400DN 1,000SN 100RA S 30,000 DT ET 1,500DT3,000ET S 18,000 1,000DT + 2,000?? + 1,500DN + 2,500SN + 300RA 50,000 S15 10 25 [4] DT ET DN SN RA 30 DT 2 0 ET 2 0 DN 20, SN 2 0, RA 0 [10-14] The situation. Advertising firm Night & Day, Inc. (NDI) has been hired to conduct an ad campaign for a client. After considering all the possible advertising media and the target market, NDI has limited next month's ads to 5 sources (listed in the table below), each of which reaches a different number of potential customers, costs a certain amount, and has its own "exposure quality." Exposure quality units measure the relative value of one ad in each source and take into account factors such as audience demographics, image presented, and ad quality Potential Customers Cost per Maximum Times Advertising Source Daytime TV Exposure Ad (S)Available per Month Quality Units 1,500 Reached per Ad 1,000 2,000 1,500 2,500 15 65 (1-min. commercial) Evening TV 3,000 10 90 (30-sec. commercial) Daily Newspaper 400 25 40 (full page ad) Sunday Newspaper 1,000 60 (1/2 page color) Radio 300 100 30 20 (30 second spot) NDI's goal is to maximize the total exposure quality from the ad campaign. The client has given NDI an advertising budget of $30,000 - see constraint [1] - and has imposed several restrictions on its use. Specifically, at least 10 TV commercials must be used, but no more than $18,000 may be spent on these commercials - see constraints [2-3]. Also, the client wants at least 50,000 potential customers to be reached through all sources - see constraint [4]. Finally, the fourth column of the table above gives limits on the number of times each advertising source may be used in a month - see constraints [5-9] LP Formulation: NDI has 5 decisions to make: . DT number of Daytime TV ads to run . ET number of Evening TV ads to run . DN number of Daily Newspaper ads to run SN number of Sunday Newspaper ads to run RAnumber of Radio Ads to run Maximize 65DT + 90ET 40DN60SN 20RA subject to: 1,500DT3,000ET 400DN 1,000SN 100RA S 30,000 DT ET 1,500DT3,000ET S 18,000 1,000DT + 2,000?? + 1,500DN + 2,500SN + 300RA 50,000 S15 10 25 [4] DT ET DN SN RA 30 DT 2 0 ET 2 0 DN 20, SN 2 0, RA 0 [10-14]