Optimization Models

Duality Theory

Read carefully every statement and answer only what is asked. Show your work. The managing sport company at a university is making plans for distributing tickets to the upcoming regional football championship. The up to 20,000 available seats will be divided between the media, competing universities, and the general public. Media people are admitted free, but the company receives $50 per ticket from universities and $100 per ticket from the general public. At least 2000 tickets must be reserved for the media, and at least half as many tickets should go to the competing universities as to the general public. Within these restrictions, the company wishes to find the allocation that raises the most money. (a) State the problem as an LP, (b) find the dual counterpart to the company's problem, and give an interpretation for the dual variables (e) Provide an optimal solution to both problems (d) According to duality theory, - which primal constraints constitute real limitations to the company? - What's the real value of an extra seat in the stadium? What would be the change to the funds raised if extra seats are allocated to the media? Read carefully every statement and answer only what is asked. Show your work. The managing sport company at a university is making plans for distributing tickets to the upcoming regional football championship. The up to 20,000 available seats will be divided between the media, competing universities, and the general public. Media people are admitted free, but the company receives $50 per ticket from universities and $100 per ticket from the general public. At least 2000 tickets must be reserved for the media, and at least half as many tickets should go to the competing universities as to the general public. Within these restrictions, the company wishes to find the allocation that raises the most money. (a) State the problem as an LP, (b) find the dual counterpart to the company's problem, and give an interpretation for the dual variables (e) Provide an optimal solution to both problems (d) According to duality theory, - which primal constraints constitute real limitations to the company? - What's the real value of an extra seat in the stadium? What would be the change to the funds raised if extra seats are allocated to the media