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Let t1:- Advertisements on television in first 10 min.s
t2:- Advertisements on television after 10 min.s
r1:- Advertisements on radio in first 15 min.s
r2:- Advertisements on radio after 15 min.s
n1:- Advertisements in newspaper in first 20 min.s
r2:- Advertisements in newspaper after 20 min.s

Objective Function:-
Maximize:- E=90*t1+55*t2+25*r1+20*t2+10*n1+5*n2

Subject to:-             r1+r2>=2*(t1+t2)         10000(t1+t2)+3000(r1+r2)+1000(n1+n2)<=279000
t1<=10                   t1+t2<=20                4000t1+1500t2+2000r1+1200r2+1000n1+800n2>=100000
t1+t2<20                 t1+t2>=14                          Assuming second condition will automatically achieve after min. lim
r1<=15                   r1+r2<=33
n1<=20                   n1+n2>=30                             r1=15
                                                               n1=20

Varibles t1              t2           r1          r2           n1           n2
Optimum values      10         6.35          15           18        16.5            0
Coefficients        90           55          25           20         10             5   2149.25

Constraints
                     1                                                                        10
                     1            1                                                        16.35   <
                                              1                                               15   <=
                                                                        1                   16.5   <=
                                              1            1           -2          -2   7.11E-15   >=
                     1            1                                                        16.35   >=
                                              1            1                                  33   <=
                                                                       1            1       16.5   >=
                10000         10000        3000        3000         1000         1000    279000
                 4000          1500        2000        1200         1000          800    117625    >=
                                              1                                               15
                                                                       1                    16.5
0n2>=100000
utomatically achieve after min. limits..




                    10
                    20
                    15
                    20
                     0
                    14
                    33
                    30
                279000
                100000
                    15
                    20

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Book2

  • 1. Let t1:- Advertisements on television in first 10 min.s t2:- Advertisements on television after 10 min.s r1:- Advertisements on radio in first 15 min.s r2:- Advertisements on radio after 15 min.s n1:- Advertisements in newspaper in first 20 min.s r2:- Advertisements in newspaper after 20 min.s Objective Function:- Maximize:- E=90*t1+55*t2+25*r1+20*t2+10*n1+5*n2 Subject to:- r1+r2>=2*(t1+t2) 10000(t1+t2)+3000(r1+r2)+1000(n1+n2)<=279000 t1<=10 t1+t2<=20 4000t1+1500t2+2000r1+1200r2+1000n1+800n2>=100000 t1+t2<20 t1+t2>=14 Assuming second condition will automatically achieve after min. lim r1<=15 r1+r2<=33 n1<=20 n1+n2>=30 r1=15 n1=20 Varibles t1 t2 r1 r2 n1 n2 Optimum values 10 6.35 15 18 16.5 0 Coefficients 90 55 25 20 10 5 2149.25 Constraints 1 10 1 1 16.35 < 1 15 <= 1 16.5 <= 1 1 -2 -2 7.11E-15 >= 1 1 16.35 >= 1 1 33 <= 1 1 16.5 >= 10000 10000 3000 3000 1000 1000 279000 4000 1500 2000 1200 1000 800 117625 >= 1 15 1 16.5
  • 2. 0n2>=100000 utomatically achieve after min. limits.. 10 20 15 20 0 14 33 30 279000 100000 15 20