Question
In: Statistics and Probability
A system consists of three machines and two repairmen. At most two machines can operate at...
A system consists of three machines and two repairmen. At most two machines can operate at any time. The amount of time that an operating machine works before breaking down is exponentially distributed with mean 5 hours. The amount of time that it takes a single repairman to x a machine is exponentially distributed with mean 4 hours. Only one repairman can work on a failed machine at any given time. Let X(t) be the number of machines in working order at time t.
a) Calculate the long-run probability distribution of X(t).
b) In the long run, what fraction of time are both repairmen busy?
c) If an operating machine produces 100 units of output per hour, what is the long run output per hour of the system?
Solutions
orchestra answered 2 years agoRelated Solutions
: A production system has three production machines. Machine A consists one component with constant failure...
: A production system has three production machines. Machine A
consists one component with constant failure rate of 0.000512
failures per day. Machine B consists of two components; this
machine works if one or more of its components work; each one of
these components has constant failure rate of 0.000725 and 0.000618
failures per day respectively. The third production machine
consists of two components; the production in this machine stops if
any of these two components stop; and one of...
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers....
The distribution system for the Herman Company consists of three
plants, two warehouses, and four customers. Plant capacities and
shipping costs per unit (in $) from each plant to each warehouse
are as follows:
Warehouse
Plant 1
2
Capacity
1
4
7
450
2 8
5
600
3
5
6
380
Customer
Warehouse
1
2
3
4
1
6
4
8
4
2 3
6 7 7
Demand
300
300
300
400
Formulate the linear programming model to minimize the cost of
shipping...
A manufacturer has three machines A, B, and C. Machines A and B can be operated...
A manufacturer has three machines A, B, and C. Machines A and B
can be operated for at most 12 hours whereas machine C must be
operated for at least 5 hours a day. These three machines produce
only two items X and Y. Product X requires 1 hour from machine A,
two hours from machine B and 1 hour from machine C. Product Y
requires 2 hours from machine A, one hour from machine B and 1.25
hours from...
A factory has three machines capable of producing widgets. All three machines together can produce 191...
A factory has three machines capable of producing widgets. All
three machines together can produce 191 widgets per hour. Machine A
and machine B together can produce 129 widgets per hour, while
machine A and machine C can together produce 137 widgets per hour.
How many widgets per hour can each machine produce?
A factory has three machines capable of producing widgets. All
three machines together can produce 242 widgets per hour. Machine A
and machine B together can produce...
Consider a small machine shop where each worker can operate all the machines but operates some...
Consider a small machine shop where each worker can operate all
the machines but operates some of the machines better than others.
On any given day there are a number of jobs which have to be
completed. For this situation, the problem facing management, is
how to obtain the fastest turnaround time for all jobs.
The time it takes to perform an average job for each of these
workers is as follows:
Drilling
Grinding
Lathework
Joe
5
10
6
Jack...
Metropole Inc. can produce three different products interchangeably on two machines. The accounting department provides the...
Metropole Inc. can produce three different products
interchangeably on two machines. The accounting department provides
the following information on these products:
A
B
C
Selling price per unit
$24
$36
$46
Variable costs per unit
$13
$28
$37
Units produced per machine
hour
10
12.5
20
Minimum units produced
115
none
145
Maximum units produced
240
none
220
The total machine hours available are 105.
Determine the number of machine hours per unit for each
product. (Round answers to 2...
Metropole Inc. can produce three different products interchangeably on two machines. The accounting department provides the...
Metropole Inc. can produce three different products
interchangeably on two machines. The accounting department provides
the following information on these products: A B C Selling price
per unit $23 $37 $43 Variable costs per unit $13 $29 $34 Units
produced per machine hour 10 12.5 20 Minimum units produced 115
none 145 Maximum units produced 240 none 220 The total machine
hours available are 105.
Determine the number of machine hours per unit for each product.
(Round answers to 2...
What does the economic system consists of Economic system consists of
What does the economic system consists of Economic system
consists of
Exercise 7.30 a-c Metropole Inc. can produce three different products interchangeably on two machines. The accounting...
Exercise 7.30 a-c
Metropole Inc. can produce three different products interchangeably
on two machines. The accounting department provides the following
information on these products:
A
B
C
Selling price per unit
$23
$37
$45
Variable costs per unit
$12
$29
$37
Units produced per machine
hour
10
12.5
20
Minimum units produced
125
none
165
Maximum units produced
200
none
220
The total machine hours available are 105.
Determine the number of machine hours per unit for each
product. (Round...
2. Suppose you operate a copying service that has two copy machines. After some experience, you...
2. Suppose you operate a copying service that has two copy
machines. After some experience, you find that hiring additional
workers increases your copying capacity by 500 sheets per worker
each day, up to the eighth worker. But, after you have eight
workers on staff, hiring additional workers produces no additional
pages copied.
a. Graph the APL and the MPL. [Hint: what would the MPL of the
ninth worker be? What would the APL be if nine workers were
hired?]...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- You have invested 30 percent of your portfolio in Jacob, Inc., 40 percent is Bella Co.,...
- Parallel Arrays This question is in MindTap Cengage Summary In this lab, you use what you...
- 5. You have invested 30 percent of your portfolio in Jacob, Inc., 40 percent is Bella...
- JAVA Write a test program that prompts the user to enter a series of integers and...
- (2) Cite an example on how organizations like Google, Facebook, Youtube etc collect data for image...
- The legal landscape is perpetually changing. Psychologists must remain abreast of these changes to avoid potentially...
- We are evaluating a project that costs $1.68 million, has a six-year life, and has no...
ADVERTISEMENT