This document presents an optimization problem to maximize advertising revenue. The objective is to maximize revenue (E) from advertising on TV, radio, and newspapers based on time of day. There are constraints on the minimum and maximum amounts that can be spent in each time period and medium. The optimal values that maximize revenue while satisfying the constraints are: 10 units of TV ads in the first 10 minutes, 6.35 units in later TV periods, 15 units of early radio ads, 18 units of later radio ads, 16.5 units of early newspaper ads, and 0 units of later newspaper ads. The maximum revenue (E) achieved under these optimal values is 2149.25.

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