Question

1. Research has shown that for a company’s toy truck every increase of $0.10 in the price will

result in 200 fewer sales. At one point, when the price was $2.35, the company sold 18,500

trucks. A reasonable employee of the company wondered aloud what price would maximize

the revenue generated by the sale of the trucks for the company.

a.) Determine the formula of the function N(x) that gives the number of trucks sold when

the price is x dollars. Draw a graph of the function N(x).

b.) Determine the formula for the function R(x) that gives the revenue generated when

the price is x dollars. Graph y=R(x).

c.) Determine algebraically the price that yields the maximum revenue. How much

revenue is generated? How many trucks are sold at this price?

d.) Let’s say that the company wants to sell 20,000 trucks. How much should they

charge and how much revenue is generated?

e.) What is the average rate of change in revenue from x=$2.50 to x=$2.85? What is the

average rate of change from x=$3.00 to $3.25? What units are associated with the

average rate of change? Interpret each average rate of change in the context of the

given situation. What do these average rates of change tell you about the shape of the

graph of R(x)?

Answer 1

ANSWER:-

a company’s toy truck every increase of $0.10 in the price will result in 200 fewer sales.

Therefore, slope of sales curve = (0-200)/(0.1-0)

= -2000

Therefore, sales curve is represented by equation: N(x) = -2000x + b

where N(x) is the number of trucks sold, x is the price and b is the intercept.

It is also given that when the price was $2.35, the company sold 18,500 trucks.

18500 = -2000*2.35 + b

18500+4700=b

b = 23200

A) Formula for N(x) is: N(x) = -2000x + 23200

Graph

B) R(x) = N(x)*x = (-2000x+23200)*x

= -2000x² + 23200x

Revenue curve

(C) For maximum revenue, dR/dx =0

=> d(-2000x² + 23200x)/dx=0

=> -4000x+23200 = 0

=> 4000x=23200

=> x = 23200/4000

x= 5.8

Price at which revenue is maximum = $ 5.8

(D) Given  N(x) = 20000

Substituting its value in the sales curve N(x)=-2000x+23200, we get

20000 = -2000x + 23200

20000-23200=-2000x

-3200=-2000x

x = 3200/2000

x= 1.6

They should charge price, x = $ 1.6

Revenue = 1.6*20000 = $ 32,000

According to check policy we solve 1st 3 quastions,if you want remaing sollutions to answers reupload E quastion

******THANK YOU******