A factory production department consists of a large number of work cells. Each cell consists of one human worker performing electronics assembly tasks. The cells are organized into sections within the department, and one foreman supervises each section. It is desired to know many work cells should be assigned to each foreman. The foreman's job consists of two tasks: (1) provide 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 work cell. Task (1) takes 18.0 min on average per work cell 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 per work cell and must be done once per day. The plant operates one shift which is 8.0 working hr, and neither the workers nor the foreman are allowed to work more than 8.0 hr per day. Each day, the cells continue production from where they stopped the day before.
(a) What is the maximum number of work cells that should be assigned to a foreman, with the proviso that the work cells are never idle?
(b) With the number of work cells from part (a), how many idle min does the foreman have each day?