Problem 141E

A food manufacturer uses an extruder (a machine that produces bite-size cookies and snack food) that yields revenue for the firm at a rate of $200 per hour when in operation. However, the extruder breaks down an average of two times every day it operates. If Y denotes the number of breakdowns per day, the daily revenue generated by the machine is R = 1600 − 50Y 2. Find the expected daily revenue for the extruder.

Solution

Step 1 of 1

We have to find the expected value of R=1600-50Y2

Let Y denotes the no.of breakdowns per day

Given that there are 2 breakdowns on an average per day

Then

We know that E(Y2)=

Now E(R)=E(1600-50Y2 )=1600-50E(Y2 )

=1600-50()

=1600-50(4+2)

=1600-300

=1300

Hence the expected value of R is 1300 $