1. Two firms produce a homogeneous product with an inverse market demand given by P = 100 – 2Q, where Q = q₁+q₂. The first firm has a cost function given by C₁=12q₁and the second firm has a cost function given by C₂=20q₂. The firms make simultaneous output choices to maximize profit. Determine the equilibrium values of firm outputs, market output, price, and firm profits.
2. With reference to question 1, now assume that decision-making is sequential with firm 1 choosing its output first (leader) and firm 2 choosing second (follower). Determine the equilibrium values of firm outputs, market output, price, and firm profit levels.
3. In the above question, there is clearly an advantage to the firm that chooses first. How should we measure the value of the first-mover advantage? Calculate this value for the first firm relative to values in question 1.
4. Return to the situation in question 1. Suppose demand increases by 100 units at each price. Solve for the equilibrium values of firm outputs, market output, price and firm profits.

Use this mini-case to answer the following question(s). (Total marks = 100)
The Delux Nut Company produces a deluxe mix of almonds, cashews, peanuts and walnuts. The deluxe mix must contain at least 10% of each kind of nut. At least half of the mix must consist of almonds and cashews and it can contain at most 20% peanuts.
The company also produces a companion mix of cashews, walnuts and raisins. This mix must contain at least 10% cashews, at least 30% walnuts, and between 20 and 40% raisins. Raisins are available in unlimited supply at a purchasing cost of R3,60 per kilogram. The quantities of nuts available and the purchasing costs in rand per kilogram are as follows:

Both mixes are sold in 100 g packages. The company must produce at least 4 000 packages of the deluxe mix and at least 5 000 packages of the companion mix.
(a) Formulate an LP model for this problem.
(b) Solve the LP using SOLVER (NB: Please use solver for me and not LINGO)
(c) Write down the optimal purchasing plan and the associated purchasing costs.

Use only the initial printout of the optimal solution to answer the following questions. (This means that you may not change the relevant parameters in the model and do re-runs.) Explain how you arrive at your answers.
(d) The suppliers inform the company that the availability of almonds has been reduced to 200 kg and that of peanuts to 100 kg. How will this influence the optimal plan and purchasing costs? Give reasons for your answer.
(e) An extra 50 kg of walnuts can be bought at R11,00 per kg. Would you make use of this offer? Give reasons for your answer.
(f) Assume that the optimal plan is obtained from the original available quantities of nuts. The company now decides that it must produce at least 4 500 packages of the deluxe mix. Will the total purchasing costs be influenced? Give reasons for your answer.
(g) The supplier of peanuts announces a 40% increase in price. What will the effect of this be? Give reasons for your answer.

import java.util.*;

class A

{

int i, j, k;

public A(int i, int j, int k)

{

this.i=i;

this.j=j;

this.k=k;

}

public String toString()

{

return "A("+i+","+j+","+k+")";

}

}

class Main

{

public static void main(String[] args)

{

ArrayList<A> aL=new ArrayList<A>();

Random rand= new Random(1000); //1000 is a seed value

for (int p=0; p<10; p++)

{

int i = rand.nextInt(100);

int j = rand.nextInt(200);

int k = rand.nextInt(300);

aL.add(new A(i, j, k));

}

System.out.println("----- Original arraylist------");

for (A a: aL)

{

System.out.println(a);

}

System.out.println("----- Sorting by first integer-------");

/*YOUR CODE - Use anonymous interface types to sort by first integer Field in A, and then

print the resulting ArrayList */

System.out.println("----- Sorting by second integer-------");

/*YOUR CODE - Use anonymous interface types to sort by the second integer Field in A, and then

print the resulting ArrayList */

System.out.println("----- Sorting by third integer-------");

/*YOUR CODE - Use anonymous interface types to sort by the third integer Field in A, and then

print the resulting ArrayList */

}

}

Ideal Output:

----- Original list ------- A(87,135,276) A(24,192,149) A(41,45,164) A(50,179,259) A(72,183,36) A(75,46,202) A(23,41,222) A(71,189,202) A(93,142,49) A(42,35,176) ----- Sorting by first integer------- A(23,41,222) A(24,192,149) A(41,45,164) A(42,35,176) A(50,179,259) A(71,189,202) A(72,183,36) A(75,46,202) A(87,135,276) A(93,142,49) ----- Sorting by second integer------- A(42,35,176) A(23,41,222) A(41,45,164) A(75,46,202) A(87,135,276) A(93,142,49) A(50,179,259) A(72,183,36) A(71,189,202) A(24,192,149) ----- Sorting by

1)(a) Patty Stacey deposits $2800 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 10%, compounded annually. (Round your answer to the nearest cent.)
$

(b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $2800 deposits at the end of each of the next 15 years. If the interest rate is 10%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)
$

(c) Does Patty or her husband have more IRA money?

PattyPatty's husband

2)

A sinking fund is established to discharge a debt of $60,000 in 20 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 8%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

1. At a price of $4, quantity supplied is 100; and at a price of $6, quantity supplied is 120. Using
   the midpoint formula, compute the price elasticity of supply is and explain supply is elastic or inelastic. What is the elasticity of supply based on percentage method? Marks 4

1. At a price of $4, quantity demanded is 100; and at a price of $6, quantity demanded is 120. Using the midpoint formula, the price elasticity of demand is ________ and demand is ________.

A) 0.1; inelastic

B) 0.45; inelastic

C) -2.2; elastic

D) -10; elastic

2.  In economics, scarcity means that

A) A shortage of a particular good will cause the price to fall.

B) A production possibilities curve cannot accurately represent the trade-off between two goods.

C) Society's desires exceed resources available.

D) The market mechanism has failed.

3 . To calculate the slope of a line, find the vertical distance between two points and divide it by the horizontal distance between the same two points. TRUE OR FALSE

1. The current price of one share of a certain stock is 100.

The price of a one-year call option on the stock with a strike price of 105 is 10.

The risk-free interest rate is 5.884% and the stock’s dividend yield is 2.02%

Mr. John would like to create a synthetic long put option on the stock with a strike price of 105 and one year to maturity, using:

• Stock
• Call option
• Cash

Determine the amount of cash and the number of shares of stock Smith will need to create the synthetic put and demonstrate that the portfolio replicates the payoff of a long put option.  Also, determine the price of the synthetic put.

Hi. I'm trying to write a program that uses dynamic memory management to create two arrays. splice() must create the third array and return a pointer to main(). Main() must capture the pointer returned from the splice() function.

Sol'n so far, I get the results of the first and second array, but it isn't showing the results of the spliced function:

#include <iostream>

using namespace std;

// Function int* splice() inserts the 2nd array into 1st array starting at int numOfElements
int* splice(int *array1, int *array2, int size1, int size2, int numOfElements)
{
   int *result = new int[size1 + size2];
   for (int i = 0; i < numOfElements; i++)
       *(result + i) = *(array1 + i);
   for (int i = 0; i < size2; i++)
       *(result + numOfElements + i) = *(array2 + i);
   //Line 13 will copy ith element of the second element into numOfElements + ith position in the final array.
   for (int i = numOfElements; i < size1; i++)
       *(result + size2 + i) = *(array1 + i);
   system("pause");
   return result;
}

int main()
{

int size1, size2, numOfElements;
   cout << "Enter the size of the first array: ";
   cin >> size1;
   cout << "Enter the size of the second array: ";
   cin >> size2;
   cout << "Enter the number of elements of the first array to be copied before splice: ";
   cin >> numOfElements;

srand(100);
   int *array1 = new int[size1];
   int *array2 = new int[size2];
   for (int i = 0; i < size1; i++)
       *(array1 + i) = rand() % size1;
   for (int i = 0; i < size2; i++)
       *(array2 + i) = rand() % size2;

cout << "The contents of the first array is: " << endl;
   for (int i = 0; i < size1; i++)
   {
       cout << *(array1 + i) << "\t";
       if ((i + 1) % 10 == 0)
           cout << endl;
   }
   cout << endl << "The contents of the second array is: " << endl;
   for (int i = 0; i < size2; i++)
   {
       cout << *(array2 + i) << "\t";
       if ((i + 1) % 10 == 0)
           cout << endl;
   }
   int *array = splice(array1, array2, size1, size2, numOfElements);

cout << "The contents of the spliced array is: " << endl;
   for (int i = 0; i < size1 + size2; i++)
   {
       cout << *(array + i) << "\t";
       if ((i + 1) % 10 == 0)
           cout << endl;
   }

    delete[] array1;
   delete[] array2;
   delete[] array;

   //the values are deleted, but the pointers still exist
}

Step 1:

Create a new Java project in NetBeans called “Wedding1”

Step 2:

Use appropriate data types to store the following information:

• The names of the bride and groom
• The total number of guests at the wedding
• The square footage of the location (must be accurate to 0.1 square feet).
• The names of each song in the DJ's playlist. You should use an ArrayList of Strings to store this, and the user should be able to enter as many song names as they wish.
• The number of guests per square foot of the location.

Step 3:

Add static methods to:

• Prompt the user for the names of the bride and groom
• Prompt the user for number of guests at the wedding
• Prompt the user for the square footage of the location
• Prompt the user for names of each song in the DJ's playlist
• Calculate and display the number of guests per square foot of the location.

Step 4:

Add functionality to:

• Save all data to a file called wedding.txt
• Load and display the contents of this file

Note: please use basic exception handling (i.e. a try block) when attempting to access a file.

Step 5:

Add logic to your main() method that uses all of the methods you’ve created in order to prompt the user for values, store their responses, save those values to a file, and display the contents of the file.

To see for yourself how the central limit theorem works, let's say we have a normal distribution (with mean =100 and standard devation = 20). Let's generate some random samples of various sizes from this distribution. We can do this in excel using =norm.inv(rand(),100,20) and it will randomly generate numbers from this distribution. I generated four samples of size 5, 10, 20 and 30, and got the means of 124 (n=5); 91 (n=10); 105 (n=20); 103 (n=30). If I continue to increase the sample size, my average values should converge to the mean of 100. Now you try. Pick a distribution and generate some sample sizes to prove this to yourself. Post and discuss your results.