Suppose there is a two$-$machine line, where each machine has a $1$ minute operation time. There is also a buffer with $1$ Kanban card between the machines. Part $1($ALREADY GOT THE ANSWERS, see below with explanation$)$

a$)$ How many parts are produced in the $1$st hour? Assume the buffer is empty at time $0.$

R: $59,$ Machine $1$ and $2$ can both produce $60$ parts$/$hour$.$ However, machine $2$ must wait $1$ minute before there is a part two work on$.($THAT$\text{'}$S CORRECT$)$

b$)$ How many parts are produced in the second hour?

R: $60,$ Now since the buffer machine $2$ is continuously fed by machine $1,$ production rate reaches $60.$ However, the buffer is still empty. $($THAT$\text{'}$S CORRECT$)$

Part $2($NEED THE CORRECT ANSWERS$)$

Suppose now that Machine $1$ now fails every hour, $10$ minutes into the hour, for $10$ minutes.

a$)$ How many parts are produced in the first hour? Assume the buffer is empty..

R: $49-($THAT$\text{'}$S CORRECT$)$

b$)$ How many parts are produced if we increase the Kanban count from $1$ to $10$ in the first hour? Assume the buffer is empty.

$*$R: $60-($IT IS INCORRECT$)$ CAN SOME CORRECT THIS

Part $3($NEED THE CORRECT ANSWERS$)$

Assuming the same conditions are still in place from part $2.$ Suppose the second machine fails $40$ minutes in the hour, every hour for $10$ minutes.

a$)$ Assuming the Kanban size is now $2,$ and the buffer is empty at time $0.$ How many parts are produced in the first hour?

$*$R: $20-($IT IS INCORRECT$)$ CAN SOME CORRECT THIS

b$)$ If we increase the Kanban to $10,$ how many parts are produced in the second hour?

$*$R: $50-($IT IS INCORRECT$)$ CAN SOME CORRECT THIS