What is the maximum and minimum value of TV commercial cost per minute for which the optimal solution found in (a) remains optimal?

Powai Inc., a media marketing firm based in Mumbai, has contracted with a company to advertise its products. The company wants its TV and radio advertising to reach certain minimum number of customers within three age-groups: over 40, between 25 and 40, and under 25. One minute of TV commercial time costs INR 90,000 and will reach (for every minute of advertisement) an average of 180,000 viewers in the over-40 group, 90,000 customers in the 25-to-40 group, and 120,000 in the under-25 group. One minute of radio commercial time costs INR 25000 and will reach (per every minute of advertisement) 40,000 listeners in the over-40 age-group, 80,000 in the 25-to-40 age-group, and 100,000 in the under-25 group. The company wants to achieve a minimum exposure of 1000,000 in the over-40 group, 800,000 in the 25−40 age-group; the company did not have any requirement for the age group less than 25 years.

(a) Formulate an appropriate linear programming model and solve it graphically to find the minimum cost that is required to meet the constraints. Identify the optimal number of minutes of advertisements in TV and radio.

(b) By how much will the cost increase if the minimum exposure in the over-40 age group is increased by another 1000 people?

(c) What is the maximum and minimum value of TV commercial cost per minute for which the optimal solution found in (a) remains optimal?

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