Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintained at 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After 1 minute the temperature of the bar is 90° C. After 2 minutes the bar is removed and instantly transferred to the other container. After 1 minute in container B, the temperature of the bar rises 10o. How long, measured from the start of the entire process, will it take the bar to reach 99.5° C?

A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling water. How long will it take the bar to reach 80° C if it is known that its temperature increases 2° during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.) sec How long will it take the bar to reach 95° C? (Round your answer to one decimal place.) sec

the company is going to send 2 different catalogs to their customers. One of the catalogs costs 50 cents to make and is 50 pages long. The conversion rate for the catalog is 5% and each customer brings in 315 dollars. The second catalog costs 95 cents to make, is 100 pages long and each customer brings in 300 dollars from it. The profit margin is 30%. What should the conversion rate for the second catalog be to make at least the same amount of profit as the first one.

After you find the conversion rate for the second one, there is a second part of the problem. Company is planning to make a new catalog which is going to cost 10 cents more than the 100 page one. The more expensive catalog is going to be sent out to 20% of the customers while the remaining 80% are going to get the 100 page one. Assume the same 30% profit margin and 300 dollar profit from each customer. What should the conversion rate for the new catalog be in order to receive the same profit at the end?

Implement a generic queue.  Use the code below for main().

main()

{

int i, x;

float y;

char z;

Queue<int> A;

Queue<float> B;

Queue<char> C;

ifstream in;

in.open("int.txt");

for (i = 0; i < 100; i++){

        in >> x;

        A.enqueue(x);

    }

cout << A.dequeue() << endl;;

for (i = 0; i < 12; i++)

        A.enqueue(i);

cout << A.dequeue() << endl;

cout << A.dequeue() << endl;

cout << "Dequeueing: "<< A.dequeue()<< endl;

while (!A.isEmpty())

     cout  << A.dequeue() << "  ";

if (A.isEmpty())

      cout << "Integer Queue Is Empty "  << endl;

in.close();

cout << endl << "Now for the floating point numbers...." << endl;

in.open("float.txt");

for (i = 0; i < 100; i++){

        in >> y;

        B.enqueue(y);

    }

cout << "Here are the first ten:" << endl;

for (i = 0; i < 10; i++){

    cout << B.dequeue() << endl;

    }

in.close();

in.open("char.txt");

for (i = 0; i < 100; i++){

        in >> z;

        C.enqueue(z);

    }

cout << "Here are the characters" << endl;

while (!C.isEmpty()){

    cout << C.dequeue();

    }

in.close();

}

Programming Task 1:

Please use the following framework to implement a class for partially filled arrays.

class PartiallyFilledArray

{

     double[] content;          // content of the array

     int size;                  // actual size of the array

     // creating an array whose physical size is 100

     PartiallyFilledArray()

     {

           // your implementation

     }

     // creating an array whose physical size is given by maxSize

     PartiallyFilledArray(final int maxSize)

     {

           // your implementation

     }

     // insertion

     boolean insert(_____________________)

     {

           // your implementation

     }

     // deletion

     boolean delete(_____________________)

     {

           // your implementation

     }

     // displaying all elements

     void display()

     {

           // your implementation

     }

}

Programming Task 2:

Please use the above class to create an empty partially filled array whose maximum size is 2000. (1) Consecutively add 20 different random integer values ranging from -100 to 100 to the array and display the content. (2) Delete the first 3 elements and display the content. Notice that you should not directly use the internal data field of PartiallyFilledArray in your test code.

Consider a forward contract on gold. Each contract covers 100 ounces of gold and matures one year from now. Suppose it costs $2 per ounce per year to store gold with the payment being made at the end of the year. Assume that the spot price of gold is $1300 per ounce, the continuously compounded risk-free interest rate is 4% per annum for all maturities.

a) In the absence of arbitrage, find the current forward price. Show your calculations.

b) Assume you immediately sell one contract. What is the value of your position in 3 months’ time if the gold spot price has fallen to $1200 per ounce and interest rates have not changed? Show your calculations.

The table below shows the total cost and marginal cost for Chrissy's Costumes, a perfectly competitive firm producing different quantities of children's costumes. The market price of costumes is $15.00.

     Chrissy's Costs of Production

Instructions: Enter your answers as a whole number.

a. If the market price is $15.00 per costume, how many costumes should Chrissy's Costumes make?

      costumes

b. If the market price for costumes falls to $12.00 per costume, how many costumes should Chrissy's Costumes make now?

       costumes

3. James is a producer in a monopoly industry. His demand curve, total revenue, curve, marginal revenue curve and total cost curve are given as follows:

Q=100-4P

TR=25Q-0.25Q²

MR=25-0.5Q

TC=6Q

MC=6

a. (4 points) How much output will James produce?

b. (4 points) What price will James charge per unit of output?

c. (4 points) How much profit will James make?

d. (8 points) If this was a competitive firm. Calculate the profit maximizing price and quantity and compare with price and quantity under monopoly.

e. (6 points) Calculate the amount of deadweight loss incurred because James is a monopolist and not perfectly competitive firm.

Production/Cost Exercises
1. The following is a short-run production table for a firm with labor as its only variable input.
Wage = $ 200
Capital = 100 units
Capital Price= $40
Product Price= $120

a. Determine the following measures at all levels of output:
MPL, APL, TFC, TVC, TC, TR, AVC, ATC, AFC, MC, PROFIT
b. At what level of output is the profit maximized?
c. What kind of observations can you make about MC, price, average total cost, and profit?

Answer the following questions below based on the following monthly product cost data for a company that is selling its product in a perfectly competitive market.

1. Fill in the columns for average variable costs (AVC), average total costs (ATC) and for marginal costs (MC).

2. How much is the total fixed costs of the firm?

3. How much is the long-run equilibrium price for this firm?

4. Explain why this firm will not produce if the price in the market for the product was $2.60?

5. At a market price of $6, what quantity would this firm produce and what would be their profit?

Please provide correct answers.