Radiant requires cargo planes for the transportation of their goods and has approached VIP Transportation Company for this specific purpose. VIP has presented two options of cargo$|$ planes $-$ WT$88$ and BH$54$ and has provided comprehensive cost$-$related information for both of them.

$\backslash$table$[[,$Personnel Cost,Fuel Cost,Maintenance Cost$],[$WT$88,1500,1250,1150],[$BH$54,1550,1550,1100]]$

Radiant Airlines has a clear plan in place for allocating funds towards personnel, fuel, and maintenance expenses. They are $-$ Radiant has $$240,000$ to spend on personnel costs, $$160,000$ on fuel, and $$80,000$ in maintenance costs. To ensure maximum efficiency, they require a minimum of three planes for each type, with two options available: the WT$88,$ boasting a weight capacity of $55$ tons, and the BH$54,$ capable of transporting up to $65$ tons. Through the implementation of Linear Programming, Radiant Airlines determines the necessary information required for optimal operations.

$($a$)$ What is the maximum amount Radiant can carry, given their budget constraint?

$($b$)$ How many WT$88$ and BH$54$ radiant should hire to carry the maximum amount?

Keep in mind that the number of WT$88$ should be at least twice the number of BH$54.$