For problems 1-3, formulate the optimization problems in the following mathematical format. (You do not have...

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For problems 1-3, formulate the optimization problems in the following mathematical format. (You do not have to solve them!) minimize f(x) subject to: a(x) = 0 cj (x) 0 for i = 1, 2,...,p (1) (2) for j = 1, 2,..., q (3) 1. An airline company in India uses A320 aircraft to fly passengers from New Delhi to Mumbai. Though the maximum seating capacity of the aircraft is 180, the airline observes that on average it flies only 130 passengers per flight. The regular fare between the two cities is Rs. 15,000. From the market survey, the company knows that for every Rs. 300 reduction in fare, it would attract an additional four passengers. The company would like to find a fare policy that would maximize its revenue. Formulate this as an optimization problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic programming problem. 2. We would like to determine the area of the largest rectange that can be inscribed in a circle of radius 5 cm. Formulate this as an optimiza- tion problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic pro- gramming problem. 3. A traveling salesperson has to start from city A, cover all other n number of cities, and then come back to city A. The distance between the ith and jth cities is given by Yij. How could one plan the route so to cover the minimum distance? Formulate this as an optimiza- tion problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic pro- gramming problem. For problems 1-3, formulate the optimization problems in the following mathematical format. (You do not have to solve them!) minimize f(x) subject to: a(x) = 0 cj (x) 0 for i = 1, 2,...,p (1) (2) for j = 1, 2,..., q (3) 1. An airline company in India uses A320 aircraft to fly passengers from New Delhi to Mumbai. Though the maximum seating capacity of the aircraft is 180, the airline observes that on average it flies only 130 passengers per flight. The regular fare between the two cities is Rs. 15,000. From the market survey, the company knows that for every Rs. 300 reduction in fare, it would attract an additional four passengers. The company would like to find a fare policy that would maximize its revenue. Formulate this as an optimization problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic programming problem. 2. We would like to determine the area of the largest rectange that can be inscribed in a circle of radius 5 cm. Formulate this as an optimiza- tion problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic pro- gramming problem. 3. A traveling salesperson has to start from city A, cover all other n number of cities, and then come back to city A. The distance between the ith and jth cities is given by Yij. How could one plan the route so to cover the minimum distance? Formulate this as an optimiza- tion problem in the format above. Identity whether this is a nonlinear programming problem, linear programming problem, or quadratic pro- gramming problem.