*python creating objects with overloaded operators

Creating objects with overloaded operators allows you to use the object like a built in data type. In this lab, you will create a fraction class. By overloading its operators, you can easily use your class to solve mathematical problems related to fractions.

Part 1: Complete Fraction Class

Complete the implementation of the Fraction class provided below.

class Fraction:
#Constructor. Puts fraction in simplest form
def __init__(self,a,b):
self.num = a
self.den = b
self.simplify()
#Print Fraction as a String
def __str__(self):
if self.den==1:
return str(self.num)
else:
return str(self.num)+"https://www.sweetstudy.com/"+str(self.den)
#Get the Numerator
def getNum(self):
return self.num
#Get the Denominator
def getDen(self):
return self.den
#Give Numerical Approximation of Fraction
def approximate(self):
return self.num/self.den
#Simplify fraction
def simplify(self):
x = self.gcd(self.num,self.den)
self.num = self.num // x
self.den = self.den // x
#Find the GCD of a and b
def gcd(self,a,b):
if b==0:
return a
else:
return self.gcd(b,a % b)
#Complete these methods in lab
def __add__(self,other):
return 0
def __sub__(self,other):
return 0
def __mul__(self,other):
return 0
def __truediv__(self,other):
return 0
def __pow__(self,exp):
return 0

Complete Implementation of the following methods. All of these methods will return an instance of the Fraction class.

Part 2: Fraction Problems

Create a file lab3.py. In this file, use your fraction class to implement functions for each of the following formula. You program should ask the user for the value of n to use in the summations.

Remember that a summation symbol just tells you to add all the values in a range.

sum from k equals 1 to 5 of k equals 1 plus 2 plus 3 plus 4 plus 5 equals 15

Write functions for each of the below expressions.

Harmonic Series:
Two:
Zero:
Partial Riemann Zeta:

Your program will ask for n as input. Compute each of the functions for the given input n. When computing the Riemann Zeta function, print values for b=2,3,4,5,6,7,8.

Verify that the input is a valid number. If it is not, ask repeatedly until a valid number is given.

Once you have been given a valid input, print out the values of each of the functions in the order H, T, Z, R. See below execution trace for exact layout.

Scoring

Part 1
- 6pts – Add
- 6pts – Subtract
- 6pts – Multiply
- 6pts – True Divide
- 6pts – Power
Part 2
- 10pts – H Function
- 10pts – T Function
- 10pts – Z Function
- 10pts – R Function

Example Execution Trace

Welcome to Fun with Fractions!
Enter Number of iterations (integer>0):
Bad Input
Enter Number of iterations (integer>0):
10
H(10)=7381/2520
H(10)~=2.92896825
T(10)=2047/1024
T(10)~=1.99902344
Z(10)=1/1024
Z(10)~=0.00097656
R(10,2)=1968329/1270080
R(10,2)~=1.54976773
R(10,3)=19164113947/16003008000
R(10,3)~=1.19753199
R(10,4)=43635917056897/40327580160000
R(10,4)~=1.08203658
R(10,5)=105376229094957931/101625502003200000
R(10,5)~=1.03690734
R(10,6)=52107472322919827957/51219253009612800000
R(10,6)~=1.01734151
R(10,7)=650750820166709327386387/645362587921121280000000
R(10,7)~=1.00834915
R(10,8)=1632944765723715465050248417/1626313721561225625600000000
R(10,8)~=1.00407735

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July 1, 2023

81) If the marginal cost of producing a television is constant at $200, then a firm should produce this item.

A) only if the marginal benefit it receives is greater than $200 plus an acceptable profit margin.

B) as long as the marginal benefit it receives is just equal to or greater than $200.

C) as long as its marginal cost does not rise.

D) until the marginal benefit it receives reaches zero.

82) Which of the following is an example of a "how much" decision?

A) The Pleasantville movie theatre is open only in the evenings. The theatre's manager is debating whether to add daily matinee shows.

B) The Zhous have demolished their old home and are debating whether to build a ranch-style house or a Craftsman home.

C) You're planning to hold a graduation party and must decide between having your party catered or having a pot-luck.

D) Chelsea has withdrawn from the swim team to take up a full-time job.

83) Which of the following is an example of a "how much" decision?

A) Octavia is debating whether to buy a pair of Jimmy Choo shoes or Steve Madden boots.

B) Humberto has taken a second job to earn money to buy a Harley-Davidson SuperLow Sportster.

C) You plan on going to Las Vegas for your birthday and are deciding if you should fly or drive.

D) Diana is trying to decide if she should open her pet shop on Sundays.

84) Marginal cost is the ________ associated with undertaking an activity.

A) total cost

B) extra cost.

C) opportunity cost.

D) foregone cost.

85) Cassie's Quilts alters, reconstructs and restores heirloom quilts. Cassie has just spent $800 purchasing, cleaning and reconstructing an antique quilt which she expects to sell for $1,500 once she is finished. After having spent $800, Cassie discovers that she would need some special period fabric that would cost her $200 in material and time in order to complete the task. Alternatively, she can sell the quilt "as is" now for $900. What is her marginal benefit if she sells the quilt "as is" now?

A) $100

B) $900

C) She makes a marginal loss of $600, not a marginal benefit.

D) The marginal benefit cannot be determined.

86) Cassie's Quilts alters, reconstructs and restores heirloom quilts. Cassie has just spent $800 purchasing, cleaning and reconstructing an antique quilt which she expects to sell for $1,500 once she is finished. After having spent $800, Cassie discovers that she would need some special period fabric that would cost her $200 in material and time in order to complete the task. Alternatively, she can sell the quilt "as is" now for $900. What is the marginal cost of completing the task?

A) $200

B) $500

C) $1,000

D) $1,000 plus the value of her time

87) Cassie's Quilts alters, reconstructs and restores heirloom quilts. Cassie has just spent $800 purchasing, cleaning and reconstructing an antique quilt which she expects to sell for $1,500 once she is finished. After having spent $800, Cassie discovers that she would need some special period fabric that would cost her $200 in material and time in order to complete the task. Alternatively, she can sell the quilt "as is" now for $900. What should she do?

A) She should cut her losses and sell the quilt now.

B) It does not matter what she does; she is going to take a loss on her project.

C) She should purchase the period fabric, complete the task and then sell the quilt.

D) She should not do anymore work on the quilt because she has already spent too much time on it and has not been paid for that time.

88) Lionel's Lawn Care is a company that maintains residential yards. Lionel's cost for his standard package of mowing, edging, and trimming is $15, and he charges $25 for this service. For a total price of $40, Lionel will also trim shrubs, a service that adds an additional $10 to the total cost of the standard package. What is Lionel's marginal benefit if he sells the standard package?

A) $10

B) $15

C) $25

D) $40

89) Lionel's Lawn Care is a company that maintains residential yards. Lionel's cost for his standard package of mowing, edging, and trimming is $15, and he charges $25 for this service. For a total price of $40, Lionel will also trim shrubs, a service that adds an additional $10 to the total cost of the standard package. What is Lionel's marginal cost of adding the shrub-trimming service to the standard package?

A) $10

B) $15

C) $25

D) $40

90) Lionel's Lawn Care is a company that maintains residential yards. Lionel's cost for his standard package of mowing, edging, and trimming is $15, and he charges $25 for this service. For a total price of $40, Lionel will also trim shrubs, a service that adds an additional $10 to the total cost of the standard package. Should Lionel continue to offer the shrub-trimming service?

A) Yes, his marginal benefit is greater than his marginal cost.

B) Yes, but only if he raises the price of the standard package.

C) No, his marginal benefit is less than his marginal cost.

D) More information is needed for Lionel to make this decision.