Question

(b) Two competing television networks, A and B, are scheduling 1-hr programmes in the same peak time period. Network A can schedule one of three possible programmes (A), and network B can schedule one of four possible programmes (B;). Neither network knows which programme the other will schedule. Both networks ask the same outside polling agency to give them an estimate of how all possible pairings of the programmes will divide the viewing audience. The agency gives them each the following table, whose (Ai,B;) entry is the percentage of the viewing audience that will watch network A if network A's programme Ai is paired against network B's programme Bj. B1 B2 B3 B4 A1 60 20 30 30 55 Az 50 75 45 80 Az 70 45 35 50 Find, using two methods, the programme that each network should schedule in order to maximise its viewing audience. [8 Marks]

Answer 1

Bi A, c C C 60 20 B2 B3 By 30 55 5. 45 Az کی۔ U O O Row Reduction:- Bi B2 40 B 30 By 5 addeol A 45 0 A3 TO 35 50 chose minimum in the rest of element in 15 in internection element and subtract Rest of element and online element effect. B3 30 (sa Az no A₂ So 5 © Adding 35 B2 Bi By Same dommy Row to make a pedect_matox, By By 35 25 35 a 20 th estel S. 35 Bi 60 36 AI Bz 20. 30 55 AY 0 O d) 20 30 Az Jo 75 45 80 > Az 70 45 35 50 AH > AY 0 o Ay A * v Repeat 6th step minimum element in the Rest of element 13. B By By A 30 25 10 A To 30 M C 20 B2 > o 0 o 3 > Colmn Reduction B. В», B3 By 0 yo s -35 A2 30 25 35 Az 0 Ay. ☺ Assigning Ai's to Bid's B3 By. ATO 40 30 5 A2 to Az 25 35 Ay- 0 Convert maximize problem into minimize problem... choose_maxi element is_So and subtract all element in so BBB. All 35 Br Az 15 25 15 20 60 so 25. ب ب اب اب با Cross antick Row and fick column A, 5 o -45 Az 30- 20 Ay 10 Acaigh Al By -, A2 B2 , A3 Bi Moxi(viewing qualience) = 55+75770 Any AM 80 80 80 = 200 CS Scanned with CamScanner