Doll Sales

Hastel Toys introduced a new toy, the Cooing Cuddles doll, despite market research indicating little demand for the doll. The company was still willing to produce (supply) 5,000 dolls, with a suggested retail price of $3. The actual demand at this price was about 100,000 dolls, so they sold out in days and retailers were desperate for more. Hastel promptly increased production, raised the suggested retail price, and fired their entire market research department.

With a new suggested retail price of $28, Hastel was able and willing to supply 50,000 dolls! Unfortunately, at this wildly inflated price the demand plummeted to 12,000 dolls, leaving huge surpluses piling up in retailers storerooms. Assume that both supply and demand can be modeled as linear functions of the price. If the market research department at Hastel had done its job effectively, what production level and retail price for Cooing Cuddles dolls would have been recommended; i.e. what is the equilibrium point for this supply and demand system?

1.

Considering the retail price as the input and the number of dolls produced (supplied) as the output, identify two points (ordered pairs) on the supply function.

A. (28, 50000)

B. (28, 100000)

C. (5000, 50000)

D. (3, 28)

E. (3, 12000)

F. (3, 5000)

Item at position 2

2.

Considering supply as a linear function of the retail price, calculate the slope of the supply line.

3.

Derive the equation for the supply, S, as a function of the price, p. Use function notation and give your answer in slope-intercept form.

S()=Blank p + Blank

4.

Can the supply functions, S(p), be classified as an increasing function, a decreasing function, or neither?

A. Increasing function

B. Decreasing function

C. Neither increasing nor decreasing

5.

Identify the y-intercept of the supply equation.

6.

Identify the x-intercept of the supply equation. Give your answer as a decimal rounded to two decimal places.

7.

Considering contextual restrictions on both price and supply, which of the following is the most appropriate domain for the supply function?

[0, )

(-,)

[0.22, )

(0, )

8.

Considering contextual restrictions on both price and supply, which of the following is the most appropriate range for the supply function?

[-400, )

[0, )

(-, 0]

(-, )

9

Considering the retail price as the input and the demand for the dolls as the output, identify two points on the graph of the demand function.

A. (3, 5000)

B. (12000, 100000)

C. (28, 12000)

D. (3, 100000)

E. (28, 50000)

F. (3, 28)

10.

Considering demand as a linear function of the retail price, calculate the slope of the demand line.

11.

Derive the equation for the demand, D, as a function of the price, p. Use function notation and give your answer in slope-intercept form.

D()=Question Blank p + Blank

12.

Can the demand function, D(p), be classified as an increasing function, a decreasing function, or neither?

A. Increasing function

B. Decreasing function

C. Neither increasing nor decreasing

13.

Evaluate ethe demand for the doll when it is priced at $10.

14.

At what price does the model predict a market demand for 50,000 "Cooing Cuddles" dolls? Give your answer rounded to the nearest cent.

15.

Identify the y-intercept of the demand equation.

16.

Identify the x-intercept of the demand equation. Give your answer as a decimal rounded to two decimal places.

17.

Considering contextual restrictions on both price and demand, which of the following is the most appropriate domain for the demand function?

A. (-, )

B. [0, 110560]

C. [3, 28]

D. [0, 31.41]

E. [0, 37.28]

18.

Considering contextual restrictions on both price and demand, which of the following is the most appropriate range for the demand function?

A.[110560, 0]

B. (-, )

C. [0, )

D. (-, 0]

E. [0, 110560]

19.

Solve the supply and demand system algebraically (using either substitution or elimination) to identify the "equilibrium point".

The equilibrium price (as a fraction in lowest terms) is Blank. Rounding to the nearest cent the equilibrium price would be approximately $ Blank. The number of dolls at equilibrium would then be approximately Blank(rounded to the nearest doll.)