$\backslash$table$[[\backslash$table$[[$Advertising$],[$Source$]],\backslash$table$[[$Potential Customers$],[$Reached per Ad$]],\backslash$table$[[$Cost per$],[$Ad $($$$)]],\backslash$table$[[$Maximum Times$],[$Available per Month$]],\backslash$table$[[$Exposure$],[$Quality Units$]]],[\backslash$table$[[$Daytime TV$],[(1-$min. commercial$)]],1,000,1,500,15,65],[\backslash$table$[[$Evening TV$],[(30-$sec$.$ commercial$)]],2,000,3,000,10,90],[\backslash$table$[[$Daily Newspaper$],[($full page ad$)]],1,500,400,25,40],[\backslash$table$[[$Sunday Newspaper$],[(1/2$ page color$)]],2,500,1,000,4,75],[\backslash$table$[[$Radio$],[(30$ second spot$)]],300,100,30,20]]$

NDI's goal is to maximize the total exposure quality from the ad campaign. The client has given NDI an advertising budget of $$30,000($see constraint $[1]$ below$)$ and has imposed several restrictions on its use. Specifically, at least $10$ TV commercials must be used, but no more than $$18,000$ may be spent on these commercials $($constraints $[2]-[3]).$ Also, the client wants at least $50,000$ potential customers to be reached through all sources $($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 $($constraints $[5]-[9]).$

LP Formulation: NDI has $5$ decisions to make: DT$,$ ET$,$ DN$,$ SN and RA$,$ the number of Daytime TV$,$ Evening TV$,$ Daily Newspaper, Sunday Newspaper and Radio Ads to run in the campaign, respectively. NDI's LP is as follows:

$\backslash$table$[[$Maximize$,65$DT$,+,90$ET$,+,40DN,+,75SN,+20$RA$,$Z$,],[$subject to:$,1,500DT,+,3,000ET,+,400$DN$,+,1,000SN,+100$RA$,30,000,[1]],[,$DT$,+,$ET$,,,,,,10,[2]],[,1,500DT,+,3,000ET,,,,,,18,000,[3]],[,1,000DT,+,2,000ET,+,1,500DN,+,2,500SN,+300$RA$,50,000,[4]],[,$DT$,,c,,,,,,15,[5]]]$