The current process produces $150$ glasses per day per worker. We work one $8$ hour shift and demand for glasses is $350$ per day. What is the cycle time for the glasses in minutes?

Less than $2\mathrm{.}5$

Greater than or equal to $2\mathrm{.}5$ but less than $3$

Greater than or equal to $3$ but less than $3\mathrm{.}5$

Greater than $3\mathrm{.}5$