A private taxi company in the UAE has recently procured 300 taxicabs to meet the rising demands in three cities—Dubai, Abu Dhabi, and Sharjah. Of these taxicabs, 100 are 4-seaters, 100 are 7-seaters, and 100 are 14-seater minivans.

The company has identified the maximum number of taxicabs needed in each city as follows:

City Taxicabs needed Sharjah 120 Abu Dhabi 150 Dubai 170 The table shows the daily profit in AED for each type of taxicab in each city.

Taxi type Sharjah Abu Dhabi Dubai Taxicabs available 4-seaters 1600 1800 1900 100 7-seaters 2000 1400 1800 100 14-seaters 3200 2800 3600 100 Taxicabs needed 120 150 170 Besides, each city needs at least 20 4-seater taxicabs. Determine how many taxicabs of each type need to be operational in each city to maximize profit.