(a) "Each linear programming problem that has a feasible region has an infinite number of solutions". Discuss. (7 Marks) (b) An advertising agency is preparing an advertising campaign for a group of agencies. These agencies have decided that their target customers should have the following characteristics with importance (weightage) as given below: CHARACTERISTICS WEIGHTAGE (%) AGE 25-45 years 20 Annual Income Above Sh. 80,000 Female Married 40 40 The agency has made a careful analysis of three media and has compiled the following data: MEDIA Data Item Magazine Radio Television Audience size ('000) 800 1,000 1,500 Cost per advertisement (sh) 10,000 30,000 100,000 Min. number of adverts allowed 15 10 10 Max. number of adverts allowed 25 15 15 Reader characteristics: () Age 25-45 years 70% 60% 50% (ii) Annual income above sh. 80,000 60% 50% 40% (iii) Females married 45% 40% 30% Advertising agency has earmarked a budget of sh 1,000,000 for this purpose. REQUIRED Formulate this as a linear programming mathematical model that will maximize the total expected effective exposure. (18 Marks)