A processor makes two components, A and B$,$ which are then packaged together as the final product $($each productsold contains one A and one B$).$ The processor can do only one component at a time: either it can make A or it can make B$.$ There is a setup time when switching between A and B$.$ Current plans are to make $50$ units of A then $50$ units of B$.$ The setup time for A is $2$ minutes and that for B is $3$ minutes. The unit runtime for A is $0\mathrm{.}2$ minute and that for B is $0\mathrm{.}1$ minute. The packaging of the two components takes $0\mathrm{.}3$ minute per unit of the final product. There is one operator for the processor and one for packaging. What is the batch size that makes the process balanced?