The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show.
For all shows together, total occupancy was 80%. What was the maximum amount of profit possible?

The cost of running all three shows a day is 10,000+3*5,000=25,000.

The has to be 80% occupancy of total seats. In total there are 200*3 shows=600 seats.

Out of that 80% is $$\frac{80}{100}\cdot600=420$$

Since we need to maximize the profit. We shall take the vacant 120 seat in show 3 which cost less.

The income from first show 200 * 250= 50,000

The income from second show 200 * 250= 50,000

The income form third show 80*200= 16,000

The total income is 1,16,000-25,000=91,000