Scenario 16.7 - Commencement
Every year at commencement,the president hands out diploma covers to joyous students that cross the front of the auditorium to accept the cover and a hearty handshake.Commencement exercises have averaged 850 students with a standard deviation of 70 the last several years.The bookstore can provide a box of 144 diploma covers for $2,000 but is unwilling to break bulk.Any additional diploma covers must be purchased on the black market at $15 each.
-Use Scenario 16.7 to answer the following.How many gross of diploma covers should be ordered from the bookstore?
A)3
B)4
C)5
D)6

Question

Quizplus · Accepted Answer

To calculate the number of diploma covers needed, we can use the formula: 
Number of diploma covers = Number of students + Safety stock 
Safety stock is the extra covers required in case of unexpected events such as damaged or lost covers. A common safety stock percentage is 10%.

So, 
Number of diploma covers = 850 + 10% of 850 
Number of diploma covers = 850 + 85 
Number of diploma covers = 935

Now we need to calculate the number of boxes required: 
Number of boxes = Number of diploma covers / Number of covers per box 
Number of boxes = 935 / 144 
Number of boxes = 6.49

We can't order a fraction of a box, so we need to round up to the nearest whole number. Therefore, we need to order 7 boxes from the bookstore.

Cost of ordering from the bookstore = 7 boxes x $2,000 per box 
Cost of ordering from the bookstore = $14,000

Now we need to calculate the number of additional covers required: 
Number of additional covers = Number of diploma covers - Number of covers ordered from the bookstore 
Number of additional covers = 935 - (7 x 144) 
Number of additional covers = 47

We need to order 47 additional covers on the black market. 
Cost of ordering from the black market = 47 x $15 per cover 
Cost of ordering from the black market = $705

Total cost of diploma covers = Cost of ordering from the bookstore + Cost of ordering from the black market 
Total cost of diploma covers = $14,000 + $705 
Total cost of diploma covers = $14,705

Instead of ordering 6 boxes and paying for 288 covers on the black market, it's better to order 5 boxes and pay for 215 covers on the black market. This saves $1,605 (the cost of one box). Therefore, the best choice is to order 5 gross of diploma covers (5 boxes from the bookstore) and 215 additional covers on the black market.