Diana Dazzle, programming manager for GDUB

-

TV, must plan her schedule of television

shows for next Wednesday evening. Of the nine

one

-

half hour shows listed below, she must

select exactly five for Wednesday evening. The estimated revenue (in $ million) is given below

for each show. Furthermore, the F.C.C. has classified each show as falling into one or more of

the categories of Publi

c Interest, Violence, Comedy, and Drama as given in the table below.

\fOur objective is to maximise profit by broadcasting exactly 5 shows with highest revenues on Wednesday evening, provided that follwing conditions are satisfied: 1) There must be atleast as many shows aired that are categorized as drama as there are stores aired that are categorised as comedy. 2) She cannot air more than 2 of the shows "news special: middle east", "focus on science" and " Urban action for education" 3) If Diana airs "Focus on Science", she must air either Spiderman" or law and Order" but not both. 4) If she airs four or more shows in violence category, she pays a fine of 5 million. 5) Exactly 5 shows are required to be aired. Therefore, our objective function is: Zmax = 7x1 + 6x2 + 8x3 + 5x4 + 8x5 + 3x6 + 4x7 + 7x8 + 2x9-5y subject to constraints x1 + x2 + x3 + x4 + x7 + x8 >= x1 + x4 + x5 1) i.e., x2 + x3 - x5 + x7 + x8 = 0 2) x6 + x7 + x9 = 1 5) x1 + x2 + x3 + x4 + x5 + x6 + x7 +x8 +x9 = 5 6) 0 = = = x1 + x4 + x5 1) i.e., x2 + x3 - x5 + x7 + x8 = 0 2) x6 + x7 + x9 = x1 + x4 + x5 1) i.e., x2 + x3 - x5 + x7 + x8 = 0 2) x6 + x7 + x9 = 1 5) x1 + x2 + x3 + x4 + x5 + x6 + x7 +x8 +x9 = 5 6) 0 = = = x1 + x4 + x5 1) i.e., x2 + x3 - x5 + x7 + x8 = 0 2) x6 + x7 + x9