HighFly Airlines is planning relocation of airbuses among the $5$ regions of the Caribbean to prepare for the influx of summer tourists. The following table shows the cost of moving an airbus between each pair of countries, along with the number of airbuses currently in each country and the number of airbuses needed in each country before the startHighFly Airlines has hired you to devise a relocation plan to meet the requirements of each country at minimal cost. of the summer period.

HighFly Airlines has hired you to devise a relocation plan to meet the requirements of each country at minimal cost.

$($a$)$ Write a mathematical model for the optimization problem above

$($b$)$ Write a program to solve $($a$).$