Two small scale production companies A and B plan to advertise their products on local radio or television. The advertisement budget is limited to Rs. 10,000 a month.Each minute of radio advertisement cost Rs. 15 and each minute of TV commercials cost  Rs. 300.Both the companies would like to use radio advertisement at least twice as much as TV.In the mean time,it is not practical to use more than 400 minutes of radio advertisement a month.Past experience shows that TV advertisement is estimated25 times more efficient than that of radio,formulate the linear programming problem and solve it graphically for maximizing project.
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Let r be the number of minutes of radio and t the number of minutes on TV.

r>2t; r<400; 15r+300t<10000 represent the constraints. In terms of effectiveness TV is 25 times more efficient than radio. Using t as the vertical axis and r as the horizontal axis, the lines t=(1/2)r, 15r+300t=10000, r=400 can be plotted. The lines t=(1/2)r and 15r+300t=10000 intersect when r<400. Substituting t=(1/2)r in the second equation we can see that 165r=10000, so r=2000/33, making t=1000/33 at the intersection. The area between the intersection of the two lines, the r axis, and the line r=400 represents where all the constraints are met.

Assuming r and t to be in whole minutes, we need to find the integers closest to the intersection point within the defined area. 2000/33=60 and 1000/33=30 so the advertising cost is for 60 mins of radio and 30 mins of TV:

Cost=15*60+300*30=900+9000=9900, leaving R100 under budget. But R100 will buy a further 6 minutes of radio advertising so r=66, t=30. 66 minutes is more than twice 30 so the constraint is still valid. 30 minutes of TV advertising has an efficiency equivalent of 25*30=750 radio minutes. Add 66 minutes to this and we have 816 minutes, so the combination is worth 816 minutes of radio time.

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