1) The demand function for cheese is given by F(y) = 50 - y, and the cost functions of both firms is given by C(x) = 4x.

A). What would be the output and price, considering the market for cheese is perfectly competitive?

B). What is the market price, industry output, and each firms level of production if there are two cournot firms operating in the market?

C). What is the industry output and market price if the two firms collude with one another?

A quality inspector is worrying about the defective produced in the production process. He wants to test that the average defectives produced are 145 or less. He collects a sample of 25 production runs and found that a sample mean of 150 defectives were produced with a std deviation of 20. With this information he wishes to perform a hypothesis test at 5% significance level.

The decision is to:

1. A force of 99N is applied to a 26kg lawnmower at an downward angle of 25 degrees relative to the horizontal. There is essentially no friction due to the wheels. Find the acceleration in the x direction

2. A 6 gram bullet is accelerated from rest to a speed of 261 m/s as it travels 79 cm in a gun barrel. Assuming the acceleration to be constant how large was the acceleting force

3. A 15kg box sits on a level table and a force of 83N is applied downward at an angle of 21 degrees related to the horizontal. If the coefficient of friction is 0.4 find the acceleration in the x direction

4. A 5kg blocks sits on a level table and a string runs over the edge of the table on a pulley to a mass of 6kg. Find the acceleration of the system if the coefficient of friction is 0.1

Lauren is 19 and has never owned a credit card. She plans to move off campus next semester because she's tired of living in the dorm. The apartment complex she's inquiring about runs background checks and views the credit reports of all the prospective tenant. She knows her credit score is zero, and she's worried that will keep her from getting in the apartment complex.

1. What can Lauren do to improve her chances of getting a low rate at the apartment complex?

2. Is it a bad thing to have a credit score of zero? Why or why not?

3. Should Lauren open a credit card account so she can start establishing a credit score? Why or why not?

Create program which verifies if input string is a valid variable declaration or not. Use C programming language.

- This program can only use the following variable types: char, float, and int

- Remove any newline \n from input string

- The input prompt should say ">>> "

- If input declaration is valid, it should print "Valid dec\n"

- If input declaration is invalid, it should print "Invalid dec\n"

- Make sure the identifier entered matches the rules of C identifiers

- No need to worry about value assignments (Ex. int i = 0;)

Example Runs:

• Invalid identifier.

    >>> char 3var;
    Invalid dec

• Invalid type.

    >>> double my_var;
    Invalid dec

• Valid declaration.

    >>> int my_int;
    Valid dec

Dock diving is a great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.52 m/s at an angle of 27° with respect to the surface of the water. (Assume that the +x axis is in the direction of the run and the +y axis is up.)

(a) If Sheba begins at a height of 0.78 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water?

(b) Write an expression for the velocity of Sheba, in component form, the instant before she hits the water. (Express your answer in vector form.)

(c) Determine the peak height above the water reached by Sheba during her jump.

A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.51° from the horizontal. A donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 535-N force for a distance of 159 m by means of a rope that is parallel to the ground and makes an angle of 13.1° with the track. The coefficient of friction for the cart\'s wheels on the track is 0.0127. Take g = 9.81 m/s2.

a)Find the work that the donkey performs on the cart during this process.

b)Find the work that the force of gravity performs on the cart during the process.

c)Calculate the work done on the cart during the process by friction.

Q5. You are a theater owner fortunate to book a summer box office hit into your single theater. You are now planning the length of its run. Your share of the film’s projected box office is

R = 10 W -0.25 (W)^2, where R is in thousands of dollars and W is the number of weeks that the movie runs. The average operating cost of your theater is AC =MC = $5 thousand per week.

1. To maximize your profit, how many weeks should the movie run? What is your profit?

You realize that your typical movie makes an average operating profit of $1.5 thousand per week. How does this fact affect your decision in part a above if at all?

Suppose you are a speculator who lives in a world where there are two islands: Island A and Island B. These two islands produce and trade rice. Today, the spot price for rice in both islands is trading at 320 cts/bushell and the storage costs in either island is 40 cts/bushell for a period of two weeks. Additionally, since these two islands trade, you can buy shipping to take from one island to the other one. The cost of shipping is 30 cts/bushell from one island to the other and it takes two weeks from the time it leaves one port to reach the final destination. Shipping is a complex process since it requires the grain to be loaded into containers, then stacked and secured inside the vessel along with everyone else’s cargo. Today, the 2-week forward with delivery in Island A is trading at 360 cts/bushell and the 2-week forward with delivery in Island B is trading at 340 cts/bushell. Can you arbitrage this market and how much do you stand to earn for every unit traded? (Suppose you don’t have an initial cash position, but that the interest rate is zero percent).