Johnny's Auto Services repairs damaged tires for three types of vehicles. The repair shop repairs multiple tires at a time. The processing time to repair tires depend on the size of the tire. The shop runs $220$ days a year with one $6\mathrm{.}5$ hour shift.Johnny wants a $10\%$ capacity cushion, It currently has four tire balancing machines. Based on the following information provide the number of machines needed to repair the three different types of tires.

ITEMS tire size $1$ tire size $2$ tire size $3$

$1.$ Annual Demand $150002200017500$

$2.$ Standard Processing Time $\mathrm{.}25\mathrm{.}35\mathrm{.}20$

$3.$ Average Service Needs $100250200$

$4.$ Standard Set$-$Up Time $\mathrm{.}30\mathrm{.}20\mathrm{.}25$

a$.$ What are the number of tire balancing machines is needed?