Finite Math for Business Question

Question

There is a linear relationship between the number of

units, N of a product that a company sells and the

amount of money, x, spent on advertising. If the company

spends $25,000 on advertising, it sells 400 units, and for

each additional $5,000 spent, it sells 20 units more.

(a) Calculate and interpret N(20,000).

(b) Find a formula for N(x) in terms of x.

(c) Give interpretations of the slope and the x- and y-

intercepts of N(x) if possible.

(d) Calculate and interpret N^-1(500).

(e) An internal audit reveals that the profit made by the

company on the sale of 10 units of its product, before

advertising costs have been accounted for, is $2,000.

What are the implications regarding the company's

advertising campaign?

Answer 1

N(x) = 400 when x=25 measured in thousands

N(x) = 420 when x = 30 "

(N,x)=

(400,25), (420,30) are two points on a graph with a line through them with slope = 5/20=

1/4= (x-25)/(N-400)

N-400 = 4x -100

N(x) = 4x +300

N(25) = 100+300 = 400

N(30) = 120+300= 420

N=number sold

x =thousand dollars spent on advertising

N(20)=80+300=380 sold with $20,000 advertising

N(x) = 4x +300

slope = 4 = 4 times the advertising budget measured in thousands of dollars

300 = y intercept = amount sold when advertising = $25,000

x intercept = -300/4 =-75 means if advertising budget is 250-75 = $175,000 there are zero sales, no one buys anything