STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established:

Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held.

Optimal Solution:

JAVA FRACTIONS QUESTION:

You will create a Fraction class in Java to represent fractions and to do fraction arithmetic. To get you used to the idea of unit testing, this homework does not require a main method. You can create one if you find it useful, however, we will not be grading or even looking at that code. You should be comfortable enough with the accuracy of your test cases that you do not need to use print statements or a main method to even do ad hoc “testing” of your Fraction class.

The .java template can be found here: https://gofile.io/d/iW4eGp

Steps to Follow for this question
1. Read through this entire document without opening Eclipse
2. In Eclipse, create a new project called HW7_CIT591, then create a package in the src folder called “fraction”. Create a new class in the “fraction” package named Fraction.java, and fill it with empty stubs of the methods you will write later. See the Writing Method Stubs instructions on page 5.
3. Import the provided SampleFractionTest.java into your Java project and run the tests -- all tests should fail (for now)!
4. Implement enough code in the methods in Fraction.java to pass all tests.
5. Use pen and paper (or an electronic document) to generate a list of additional test cases you will use for each method in the Fraction class. You should have a total of at least 4 distinct and valid test scenarios (with individual test cases) per method (including the ones provided).
6. Create a second testing class file named FractionTest.java and write all of the additional test cases you generated in step 5. See the Writing Unit Tests instructions on page 7.
7. Update your implementation in the methods in Fraction.java to pass all additional tests.
a. If something fails:
i. Make sure all test cases are valid
ii. Fix any mistakes in your implementation

iii. Re-run the test file
iv. Repeat these steps until all tests pass
8. Re-run both test files to make sure all tests pass

A fraction is a number of the form numerator/denominator where the numerator and denominator are integers. The denominator cannot be 0. You may assume that no user will input a denominator of 0. The Fraction class needs to have two instance variables: numerator and denominator. The methods in this class are below. They have been provided with their method signatures.
public Fraction(int numerator, int denominator)
● The constructor to create a Fraction with the given numerator and denominator.
● The constructor should set the numerator and denominator instance variables in the Fraction class.
● The constructor should also properly format negative fractions. The convention is that negative fractions have the negative in the numerator.
● For example:
o Creating a new Fraction(4, 16) would set the numerator to 4 and the denominator to 16
o Creating a new Fraction(4, -16) would set the numerator to -4 and the denominator to 16
o Creating a new Fraction(-1, -2) would set the numerator to 1 and the denominator to 2
public void reduceToLowestForm()
● Reduce the current fraction by eliminating common factors.
● That is, turn a fraction like 4/16 into 1/4 and a fraction like 320/240 into 4/3.
● Remember, the convention is that negative fractions have the negative in the numerator.
● For example:
o A fraction like 4/16 would reduce to 1/4
o A fraction like 10/-15 would reduce to -2/3
o The reduced form of any fraction that represents 0 is 0/1
▪ e.g. 0/4 reduces to 0/1

public Fraction add(Fraction otherFraction)

Add the current fraction to the given otherFraction.
● Returns a new Fraction that is the sum of the two Fractions.
● The returned Fraction must be in reduced/lowest form.
● For example:
o Adding the fraction 3/5 to the fraction 1/4 reduces to 17/20
o Adding the fraction -1/2 to the fraction 2/-3 reduces to -7/6

public Fraction subtract(Fraction otherFraction)
● Subtract the given otherFraction from the current fraction.
● That is, thisFraction - otherFraction.
● Returns a new Fraction that is the difference of the two Fractions.
● The returned Fraction must be in reduced/lowest form.
● For example:
o Subtracting the fraction 3/9 from the fraction 5/9 reduces to 2/9
o Subtracting the fraction 5/16 from the fraction 4/16 reduces to -1/16
public Fraction mul(Fraction otherFraction)
● Multiply the current fraction by the given otherFraction.
● Returns a new Fraction that is the product of this fraction and the otherFraction.
● The returned Fraction must be in reduced/lowest form.
● For example:
o Multiplying the fraction 1/2 by the fraction 2/3 reduces to 1/3
public Fraction div(Fraction otherFraction)
● Divide the current fraction by the given otherFraction.
● That is, thisFraction / otherFraction.
● Returns a new Fraction that is the quotient of this fraction and the otherFraction.
● The returned Fraction must be in reduced/lowest form.
● For example:
o Dividing the fraction 4/16 by the fraction 5/16 reduces to 4/5
public double decimal()
● Return this fraction in decimal form.
● For example:
o For the fraction 2/4, this method should return the value 0.5
o For the fraction 1/3, this method should return the approximate value 0.3333333333333333
▪ Note, to unit test double values like this, use assertEquals with a delta (see the lecture slides on Comparing Floating Point Types)

public void sqr()

● Square the current fraction.
● This method modifies the current fraction and reduces it to lowest form.
● For example:
o A fraction like 2/3 will become 4/9
o A fraction like 4/16 will become 1/16
public Fraction average(Fraction otherFraction)
● Average the current fraction with the given otherFraction.
● Return a new Fraction that is the average of this fraction and the otherFraction.
● The returned Fraction must be in reduced/lowest form.
● For example:
o Averaging the fraction 5/8 with the fraction -12/16 reduces to -1/16
public static Fraction average(Fraction[] fractions)
● Static method to average all of the fractions in the given array.
o Note, you don’t need to create an instance of the Fraction class in order to call a static method
o For example, you should be able to call this method with the class name (note upper-case in “Fraction”)
Fraction f = Fraction.average(myArrayOfFractions);
● Do not include the current fraction in the average.
● Return the average of the array.
● The returned Fraction must be in reduced/lowest form.
● If the array is empty, return a new Fraction that equals 0. That is 0/1.
● For example:
o The average of the fractions 3/4, 3/5, and 3/6 reduces to 37/60
public static Fraction average(int[] ints)
● Static method to average all the integers in the given array.
o Again, you don’t need to create an instance of the Fraction class in order to call a static method
o For example, you should be able to call this method with the class name (note upper-case in “Fraction”)
Fraction f = Fraction.average(myArrayOfInts);
● Do not include the current fraction in the average.
● Return the average of the array as a new Fraction.

● The returned Fraction must be in reduced/lowest form.
● If the array is empty, return a new Fraction that equals 0. That is 0/1.
● For example:
o The average of the ints 1, 2, 3, and 4 reduces to 5/2
@Override
public boolean equals(Object object)
● Overriden method to compare the given object (as a fraction) to the current fraction, for equality. (See the lecture slides on Testing for Equality)
● Two fractions are considered equal if they have the same numerator and same denominator, after eliminating common factors.
● This method does not (permanently) reduce the current fraction to lowest form.
● For example:
o The fraction 2/3 is equal to the fraction 2/3
o The fraction 4/16 is equal to the fraction 1/4, but the fraction 4/16 is not reduced to lowest form.

@Override
public String toString()
● Overriden method to return a string representation of the current fraction.
● A fraction like 2/3 will be represented in string form as “2/3”.
● There is a no whitespace in this string.
● If the fraction is negative, it will be expressed as “-2/3”, not “2/-3”.
Tip: You are always encouraged to write additional helper methods! We highly recommend that if you write helper methods, you test them.

Please submit all your Java classes to Codio. Make sure it is all put in the “src” folder. Included should be 3 files: your Fraction.java, your FractionTest.java, and our SampleFractionTest.java.

Problem 2 [21 marks] Consider a firm that uses two inputs. The quantity used of input 1 is denoted by ?1 and the quantity used of input 2 is denoted by ?2. The firm produces and sells one good using the production function ?(?1,?2) = 4?1 0.5 + 3?2 0.5. The final good is sold at price ? = $10. The prices of inputs 1 and 2 are ?1 = $2 and ?2 = $3, respectively. The markets for the final good and both input goods are treated as competitive markets by the firm, that is, it takes prices as given.

a) Show whether the production function has increasing, decreasing, or constant returns to scale. [2 marks]

b) Find the marginal product of each input. Show whether the production technology obeys the law of diminishing marginal products. [2 marks]

c) Draw the isoquant for an output level of 12. Clearly label the axes and the curve and show any two input bundles on the curve by indicating their coordinates. [2 marks]

d) Does the firm have convex production technology? Explain. [2 marks]

e) Find the technical rate of substitution. Does the technology show diminishing technical rate of substitution? Explain. [2 marks] Assume in the short run that ?2 is fixed at ?2 ̅̅̅ = 100.

f) Write down the firm’s profit function and the firm’s short run profit maximisation problem. Find the firm’s optimal use of input 1, the associated optimal quantity of the output good, and the firm’s profit level. [4 marks] Now consider the long run, where the quantity of input 2 can be varied.

g) According to your answer in part a), does the firm have a profit maximising plan in the long run? If no, explain why. If yes, is the plan unique? [2 marks]

h) Write down the firm’s profit function and the firm’s long run profit maximisation problem. Find the firm’s optimal use of input 1, input 2, the associated optimal quantity of the output good, and the firm’s profit level. [4 marks]

j) Explain why the profit level in the long run must be at least as high as the profit level in the short run. [1 mark]

Kuya participated in 10-K races held in several states. He provided you with the times completed by each runner. Which state did he do best and which state the worst in comparison to the group of runners for that state?

Georgia

Maine

Nevada

Ohio

Texas

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $250,000 and will yield the following expected cash flows. Management requires investments to have a payback period of three years, and it requires a 10% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Required:  

1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

Complete this question by entering your answers in the tabs below.

• Required 1

• Required 2
• Required 3

Determine the payback period for this investment. (Enter cash outflows with a minus sign. Round your Payback Period answer to 1 decimal place.)

Determine the break-even time for this investment. (Enter cash outflows with a minus sign. Round your break-even time answer to 1 decimal place.)

Determine the net present value for this investment.

4.

a. Suppose Z~Normal(0,1). Find P(1<Z<2). (3pts)

b. Suppose X~Normal(-2,1). Find P(X>0 or X<-3). (3pts)

c. Suppose X~Normal(2,4). The middle 88% of the X values are between what two values? (3pts)

Definition matching

1.Natural selection

2.phylogeny,

3.genetic drift,

4.homology,

5.continuous character,

6.wide sense heritability,

7.discontinuous character,

8.directional selection,

9.cladogenesis,

10.reverse mutation,

11.polymorphic locus,

12.gene flow,

13.population genetics,

14quantitative genetics,

A. Allele movement between populations.

B. Evolution of characteristics to make the organism more suitable.

C. Study the inheritance of polygenic characteristics.

D .It is the evolutionary history

E. Frequency change due to chance.

F. One of the homozygotes is favored.

G. It is due to a common ancestor.

H. When phenotypic variation is attributed to genetic variation.

I. Study the inheritance of one or a few genes in groups of individuals.

J. Selection that favors both homozygotes.

K. Recessive allele changes to dominant.

L. Simple relationship between phenotype and genotype.

M. It favors diversification.

N. Contributory alleles additively contribute to the phenotype

O. Any gene that has more than one allele in the population.

diversifying selection

IDENTIFY AND DISCUSS THE FOLLOWING ACRONYMS:

1.PICPA

2.IFAC

3.IASC

4.AFA

5.PFRS

6.GAAP

7.IFRS

8.ASC

9.FASB

10.PAS

Discuss the difference between GAAP and IFRS

Who are the key players in the development of Philippine GAAP? Explain their functions

Identify and Discuss the four main types of Accounting

Solve these first-order Differential Equations using an integrating factor.

1. dy/dx+2xy=0

2. dy/dx-y=5

3. dy/dx+y=x

4. (x)dy/dx+(x+1)y=3/x

5. (x^2)dy/dx=e^x-2xy