The student advisement office at the University has a student worker who copies
ID: 351197 • Letter: T
Question
The student advisement office at the University has a student worker who copies and assembles a handbook for students whenever the supply of these runs low. Past observations indicates that these handbooks are given out at the rate of 4 per day. The student worker can copy and assemble 100 per eight-hour day. The student worker is paid 3.75 $/hour and it takes .5 hour to prepare everything to produce a batch of handbooks. The cost of carrying inventory is related to handbooks that are damaged or become obsolete due to changes in the degree requirements. On average, 10% of all handbooks become unusable, and each costs $1 in materials, labor and copying costs.
a) If the office is open 250 days/year, how many handbooks should the student worker produce at a time in order to minimize costs?
b) How many days of demand will be supported by this order quantity?
c) What will be the maximum handbook inventory, assuming the minimum is zero?
d) What is the average inventory of handbooks?
Explanation / Answer
Answer a) Number of days office open = 250 days
Past observations shows 4 per day are given out. So we need overall 1000 handbooks. Since no of books in a batch is not given, I assumed 100 books in a batch.
reducing unusables = 100-10%100= 90 handbooks can be produced in 8 hours per day. and adding 0.5 hours , the total working hours become 8.5 hours in a day.
(note: I am neglecting extra 6 handboks which will also contribute to inventory cost. Counting those will increase the unusable items cost even more. So, to make calculation easier I took 90 only in the calculations).
Total money has to be paid to worker = 8.5x3.75= $31.875
total days require to assemble 1000 handbooks = 1000/90=11.11 days or 266.66 hours
For 11.11 days it becomes = $ 3.75x266.66 = $ 1000
2nd Case,if number of books in a batch = 4
reducing unusables = 4-10%4 =3.6
Total days required to produce 1000 handbooks to meet the demand = 1000/3.6 = 277.777 > 250 days
In 250 days total handbooks assembled = 250x3.6 = 900
toal working hours in a day becomes =8x4/100 +0.5=0.82 hours
Total money has to be paid in 250 days = 0.82x3.75x250 = $768.75
Note: In second case since the number of handbooks assembled are 4. they can be given out 4 per day. So, there will be no inventory cost. I took inventory cost just make the things a bit more clear that even if you consider 10% unusables its overall cost is still lesser. But in Actual answer to this question,
total cost = 4x3.75
So, in second case overall cost is minimum.
Answer b) It can fullfill the demand for 225 days as number of handbooks assembled are 900 in 250 days.
Answer c) maximum handbook inventory can be 1056 in 1st case and 0 in 2nd case
Answer d) average is 0 in 2nd case
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