Question: A factory production department consists of a large number of workcells. Each cell consists of one human worker performing electronics assembly tasks. The cells are organized into sections within the department, and each section is supervised by one foreman. It is desired to know how many workcells should be assigned to each foreman. The foreman's job consists of two tasks:

(1) providing each cell with a sufficient supply of parts that it can work for 4.0 hr before it needs to be resupplied and

(2) preparing production reports for each workcell.

Task (1) takes 18.0 min on average per workcell and must be done twice per day. The foreman must schedule the resupply of parts to every cell so that no idle time occurs in any cell.

Task (2) takes 9.0 min/workcell and must be done once per day. The plant operates one shift which is 8.0 working hours and neither the workers nor the foreman are allowed to work more than 8.0 hr/day. Each day, the cells continue production from where they stopped the day before.

(a) What is the maximum number of workcells that should be assigned to a foreman, with the proviso that the workcells are never idle?

(b) With the number of workcells from part (a) how many idle minutes does the foreman have each day?