私立中原大學八十八學年度博士班招生考試命題紙

所組別：

工業工程學系博士班

科目：

工業工程基礎科目　　--作業系統

考試時間：

06月09日第 1節

1. (Operations research)(25pts)Consider the following linear program
   　　　　　　　
   

   (a)	(5pts)Draw a graph of the constraints and shade in the feasible region. Label the vertices of the feasible region.
   (b)	(2pts)Use (a) to find the optimal solution and the optimal value.
   (c)	(3pts)Find the shadow prices in each constraint.
   (d)	(5pts)Find the ranges associated with the two coefficients of the object function.
   (e)	(5pts)Find the righthand-side ranges for the three constraints.
   (f)	(5pts)Solve this problem by the simplex method.

2. (Operations research)(25pts)A secretary receives her word proessing work. This model can be formulated by an M/M/1 queueing model. The jobs arrive with the Poisson rate of six jobs per hour, and served by the medn service time of 12 min. per job. Determine
   

   (a)	(5pts)the probabiblity that the secretary is busy.
   (b)	(5pts)the mean number of jobs waiting for her processing.
   (c)	(5pts)the mean length of time that a job can be finished after it is given to the secretary.
   (d)	(5pts)the probability that an arriving job will be completed in 40 min.
   (e)	(5pts)If the secretary can have 50 dollars for each job she finishes, but there is also a penalty 10 dollars for each job of which delay exceeds 40 min. Assume this secretary works 8 hours a day. What is her mean income for each day.

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