operation research

Q.1 Partially completed products arrive at a workstation in a manufacturing operation at a mean
rate of 40 per hour (Poisson distributed). The processing time at the workstation averages 1.2
minutes per unit (exponentially distributed). The manufacturing company estimates that each
unit of in process inventory at the workstation costs $31 per day (on the average). However, the
company can add extra employees and reduce the processing time to 0.90 minute per unit at a
cost of $52 per day. Determine whether the company should continue the present operation or
add extra employees.

Q.2 The Universal Manufacturing Company produces a particular product in an assembly line
operation. One of the machines on the line is a drill press that has a single assembly line feeding
into it. A partially completed unit arrives at the press to be worked on every 8 minutes, on average,
according to an exponential distribution. The machine operator can process an average of 10 parts
per hour (Poisson distributed). Determine the average number of parts waiting to be worked on,
the percentage of time the operator is working, and the percentage of time the machine is idle.