Question

You work as an expert in a company that is planning advertising. Your annual budget is 8.000.000 TL. You advertise on two television channels (Channel W and Channel T). Channel T's one-minute advertising fee is 20,000 TL, while Channel W's one-minute advertising fee is 45,000 TL. Due to the company policy, Channel W must be advertised at least half of the advertising time given to Channel T. According to the view rates, the advertisements given Channel W are watched at least 2,5 times more than the advertisements given to Channel T. In addition, Channel W must be advertised for at least 100 minutes. Create a linear programming model required to use your annual budget optimally.

  

Answer 1

Let the Decision Variables Be X_w = Number of minutes of Time on Channel W, and X_t = Number of minutes of Time on Time for Channel T. The objective is to maximize views subject to the budget and other constraints.

Objective function to be Maximized is

Y = 2.5*X_w + X_t where Y is the effective viewership - since we know W is watched 2.5 times more than T

Subject to the constraints as follows

• Budget for Channel W = X_w*45000. Budget for Channel T = X_t*20000. Total budget is 8,000,000. Hence Budget constraint is 45000*X_w + 20000*X_t <= 8,000,000 i.e 9*X_w + 4*X_t <= 1600.
• Channel W airtime must be at least half of Channel T. Hence viewership constraint is X_w >= X_t/2 or X_w - X_t/2 >= 0
• Minimum time allocated for Channel W is 100 minutes. Hence X_w >= 100