$4$ products $($P$1,$ P$2,$ P$3$ and P$4)$ are produced on $4$ machines $($M$1,$ M$2,$ M$3$ and M$4)$ in a flow$-$shop factory. The time for processing the products on a given machine is provided in Table$-1.$ For the sake of simplicity, assume that once a job is finished processing on a machine, it can immediately move to the next machine $($no waiting$/$ set$-$up times$),$ provided the next machine is available $($no job is currently processing on that machine$).$ You are asked to develop a schedule for the production of the $4$ Products.

All answers for this caselet need to be in integers

If the above problem is modelled as an Integer Linear Programme, then how many binary variables are present in the model?