Math 133-1404A-04 unit 1 discussion board

Page 1 of 3

MATH133 Unit 1: Linear Equations and Inequalities

Discussion Board Assignment: Version 2A

Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.

Linear Demand and Supply

1. Research linear demand and supply functions’ concepts using the AIU library or the

Internet to help you with this DB assignment.

The linear demand function is given by the linear function equation q = mp + b, where q

is the number of items demanded corresponding to the price, p, in U.S. dollars of each

item demanded, m is the slope of the linear function, and b is the q-intercept of the linear

function.

Table A

p1 q1

2 1,400

3 1,200

4 1,500

5 1,250

6 1,100

7 1,300

8 1,150

2. Choose 1 pair of numbers, (pi, qi), i = 1, 2, from each table above. You must choose the pi

and qi that are on the same row in Table A or Table B, but you may choose combinations

that are in different rows in each table. For example, if you choose 4 from the p1 column

in Table A, then you must choose 1,500 from the q1 column so that the ordered pair (4,

1,500) is chosen from Table A. Then, you can choose any of the row values from Table

B, such as (18, 150), to go with the ordered pair (4, 1,500). Make sure that your chosen

two ordered pairs of numbers from Tables A and B are different from the combinations

that are chosen by all of your classmates who have already posted.

3. Use your chosen two ordered pairs and the equation of the slope of a linear function

Table B

p2 q2

12 400

13 200

14 500

15 250

16 100

17 300

18 150

Page 2 of 3

𝑚 = 𝑞2 – 𝑞1 𝑝2 – 𝑝1

to find the slope of the linear demand function. (Show all of your work.)

4. Then, use the slope that you found in part c with the fact that q2 = mp2 + b will be a true

equation if the known values of q2, p2 and m are placed in this equation to find the correct

value for b. The value of b will be the vertical axis-intercept (the q-intercept). (Show all

of your work.)

5. State your linear demand function in the form q = mp + b, where m and b are your values

of slope and q-intercept.

6. For your specific linear demand function (that should be different from all other students

in the class), what will be the demand value when the price is p = $10 per item? (Show all

of your work.)

7. Using the techniques for solving linear inequalities, for what values of p in your demand

function will the quantity demanded, q, be less than 20 items? (Show all of your work.)

8. Suppose the supply function for these items is q = 100p +80, which means that there are

80 items already in the warehouse, and for each $1 that the price goes up, the supply will

go up 100 times (meaning 100 more will be produced). The values of q are the numbers

of items that will be available at that price, p. What is the supply when the price is $10

per item? How does this compare to your demand value when the price is $10 (from part

6, above)? (Show all of your work.)

9. Because the demand function and the supply function are both linear functions, and

because the demand linear function has a negative slope and the supply linear function

has a positive slope, these lines will intersect for some price of the item. This intersection

price is called the equilibrium price. What steps or procedures would you perform to

determine the exact equilibrium price for this situation? (Give a full explanation.)

10. What is the exact equilibrium price? (Show all of your work.)

11. Using Excel or another graphing utility, draw the graphs of both your linear demand

function model and your linear supply function model, insert those graphs into a Word

document, and attach that Word document to this Discussion Board thread. In Excel, use

Scatter with Smooth Lines and Markers to draw the straight line graphs. (There is a

tutorial showing how to draw graphs in Excel and how to insert them into your Word

document in the multimedia course materials. There is also information about how to

draw graphs in Excel in the Excel Learning Lab in the AIU Learning Center. Please

Page 3 of 3

review these tutorials to see how to draw graphs using Excel that are required in this

Discussion Board assignment.)

12. Why might it be important to know this equilibrium price? (Explain your answer.)

13. Which intellipath Learning Nodes helped you with this assignment?

Reference

Formatting math as text. (n.d.). Retrieved from the Purple Math Web site:

http://www.purplemath.com/modules/mathtext.htm