1.Equilibrium Price: Skateboards The demand for your hand-made skateboards, in weekly sales, is

q = 2p + 1000

if the selling price is $p. You are prepared to supply

q = 3p 600

per week at the price of $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus?$ per skateboard

2. Equilibrium Price: Skateboards The demand for your factory-made skateboards, in weekly sales, is

q = 7p + 50

if the selling price is $p. If you are selling them at that price, you can obtain

q = 4p 30

per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.)

3. Equilibrium Price: Cell Phones Worldwide quarterly sales of a brand of cell phones were approximately

q = p + 166

million phones when the wholesale price was $p.(a)If the cellphone company was prepared to supply

q = 9p 364

million phones per quarter at a wholesale price of $p, what would have been the equilibrium price?$ (b)The actual wholesale price was $48 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price. There is an estimated ---Select--- shortage surplus of........ million phones.

4. Equilibrium Price: Cell Phones Worldwide annual sales of a certain product were approximately

8p + 1,600

a million products when the wholesale price was $p.(a)If manufacturers are prepared to supply

q = 11p 800

million products per year at a wholesale price of $p, what would be the equilibrium price? (Round your answer to the nearest cent.)$ (b)The actual wholesale price was projected to be $100 in the fourth quarter of 2008. Estimate the projected shortage or surplus at that price. There is an estimated ---Select--- shortage surplus of -----million products.

5. A piano manufacturer has a daily fixed cost of $1,400 and a marginal cost of $1,800 per piano. Find the cost

C(x)

of manufacturing x pianos in one day.

C(x) =

Use your function to answer the following questions.(a) On a given day, what is the cost of manufacturing three pianos? $ (b) What is the cost of manufacturing the third piano that day? $ (c) What is the cost of manufacturing the 11th piano that day? $ (d) What is the variable cost?

$

What is the fixed cost? $ What is the marginal cost? $ per piano

6. Your college newspaper, The Collegiate Investigator, has fixed production costs of $68 per edition and marginal printing and distribution costs of 40 per copy. The Collegiate Investigator sells for 60 per copy.(a)Write down the associated cost function C(x) in dollars.C(x) =

Write down the revenue function R(x) in dollars.R(x) =

Write down the profit function P(x) in dollars.P(x) =

(b)What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator?$ (c)How many copies should be sold in order to break even? copies

7. The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eat-a-thon." The society will charge students 89 per serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at 17 per serving, and the $360 cost of renting the facility for the evening.(a)Write down the associated cost function C(x) in dollars.C(x) =

Write down the revenue function R(x) in dollars.R(x) =

Write down the profit function P(x) in dollars.P(x) =

(b)How many servings of pasta must the Audubon Society sell to break even? servings(c)What profit (or loss) results from the sale of 1,500 servings of pasta?$