A company plans to upgrade its data center and is comparing two types of processors for its servers. Processor A has a performance of $50$ GFLOPS and costs $$1000,$ while Processor B has a performance of $80$ GFLOPS and costs $$1500.$ The company needs a total performance of at least $400$ GFLOPS for its data centre.

$1.$ What is the minimum number of each type of processor $($A and B$)$ the company needs to purchase to acheive the required performance $?$

$2.$ What is the total cost for each option?

$3.$ Which option is more cost effective in achieving the required performance?