Gates Cleaning Co$.$ leases a vacuum cleaning system for a basic monthly fee plus an additional cost per hour used above a given minimum for each month. Given below is the information for the most recent six$-$month period on the number of machine hours of use and the total cost under this lease. July machine hours $1,389$ total cost $11,877,$ August machine hours $920,$ total cost $9,554,$ september machine hours $1,900$ total cost $14,056,$ october machine hours $1,508$ total cost $12,670,$ november $850$ total cost $9,289$ december $1,860$ total cost $13,677$ You are to provide information for planning on the variable and fixed cost elements in this contract. Use the high$-$low method to

$($a$)$ determine the variable cost per machine hour $($please show your work, solutions without proper calculations will receive NO Credit, please take answer out $2$ decimal places$)(6$ points$)$ and $($b$)$ find and prove the fixed costs $($calculations must be shown for credit$).(4$ points$)$