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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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?
Step by step
Solved in 2 steps with 10 images
