You will be tasked with designing a production line facility to assemble a new product.

The production line consists of $5$ work units that are all in sequence with each other.

It takes a certain amount of time to complete each task individually. Task $1$ takes $6$ min.$/$pc$.,$ task $2$ takes $8$ min.$/$pc$.,$ task $3$ takes $5$ min.$/$pc$.,$ task $4$ takes $7$ min.$/$pc$.$ and task $5$ takes $10$ min. pc$.$

The demand for the product is $120$ pcs$.$ per hour.

a$)$ Calculate the cycle time that would be needed to meet the demand.

b$)$ Calculate the minimum number of workstations $($work stations$)$ needed in one production line to be able to achieve a certain production capacity. What is the production capacity of one production line? Assume that each workstation can only produce $1$ piece at a time.

c$)$ How many production lines would be needed for production to keep up with demand?