Mr. Jaggi and Tony own a popular cinema hall Theatre Bollywood. The seating capacity of the hall is 1000. They select movies that are action oriented, have astrong emotional content with many lively songs and dances. Thus the demand does not vary much from movie to movie. They plan to continue this tradition in future. Last year was a good insales. It was estimated that the demand is exponentially distributed with mean of 700. For simplicity, the price of ticket may be assumed to constant at Rs. 200. This will remain thesame for the next year. J&T typically pay a charge of Rs. 120,000 per show to the film distributor. The distributor in turn makes up revenues when less than 500 seats are sold. In thatcase he effectively purchases tickets so that the total revenue to J&T equals that obtained by selling 500 seats. For example if in a show 350 customers show up, then the distributor paysback 150*200 = Rs. 30,000 to Jaggi and Tony (J&T) so that his total charge equals Rs. 90,000.
This year J&T have conducted a massive advertising campaign on the music channels ontelevision. In addition, some of the biggest stars, super stars, mega stars and item stars visited their hall leading to free publicity on news channels which of course covered this non-stopfor weeks. J&T believe that this has improved the profile of their cinema hall and expect a 20% increase in demand, that is, they expect the demand to be 1.2 times the exponentialdistribution with mean 700 per show.
a) If D denotes an exponentially distributed random variable with mean 700 (a proxy for typical demand last year), write down a single algebraicexpression for
i. the profit (revenue-cost) earned by J&T in a typical show this year as a function of D.
ii. The amount the distributor earns in a show this year as a function of D.