I. L. Pea is a well-known mail-order company. Duringthe Christmas rush (from November 1 to December 15), thenumber of orders that I. L. Pea must fill each day (five daysper week) is normally distributed, with a mean of 2,000 anda standard deviation of 500. I. L. Pea must determine howmany employees should be working during the Christmasrush. Each employee works five days a week, eight hours aday, can process 50 orders per day, and is paid $10 per hour.If the full-time work force cannot handle the day’s ordersduring regular hours, some employees will have to workovertime. Each employee is paid $15 per hour for overtimework. For example, if 300 orders are received in a day andthere are four employees, then 300 4(50) 100 ordersmust be processed by employees who are working overtime.Since each employee can fill 5806.25 orders per hour, I. L. Pea would need to pay workers 61.020516 hours ofovertime for that day. To minimize its expected labor costs,how many full-time employees should I. L. Pea employduring the Christmas rush?

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Chapter1: Combinatorial Analysis
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I. L. Pea is a well-known mail-order company. During
the Christmas rush (from November 1 to December 15), the
number of orders that I. L. Pea must fill each day (five days
per week) is normally distributed, with a mean of 2,000 and
a standard deviation of 500. I. L. Pea must determine how
many employees should be working during the Christmas
rush. Each employee works five days a week, eight hours a
day, can process 50 orders per day, and is paid $10 per hour.
If the full-time work force cannot handle the day’s orders
during regular hours, some employees will have to work
overtime. Each employee is paid $15 per hour for overtime
work. For example, if 300 orders are received in a day and
there are four employees, then 300 4(50) 100 orders
must be processed by employees who are working overtime.
Since each employee can fill
5
8
0
6.25 orders per hour,

I. L. Pea would need to pay workers 6
1
.
0
2
0
5
16 hours of
overtime for that day. To minimize its expected labor costs,
how many full-time employees should I. L. Pea employ
during the Christmas rush?

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