Answer to Question #267173 in Algebra for Osman

Question #267173

The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions for the company

R(x)= x(1190-360x)

C(x)= 4320+146x

Both have domain 1≤x≤20.

a)Form a profit function P and graph R, C, and in the same rectangular coordinate system using 3-unit intervals.

b)Discuss the relationship between the intersection points of the graph R and C and the q intercept of P

c)Determine the break-even point graphically.


1
Expert's answer
2021-11-18T11:03:23-0500

a)

if C(x) is cost function, then profit function:

"P(x)=R(x)-C(x)=-360x^2+1044x-4320"




b)

for intersection points of the graph R and C:

"-360x^2+1044x-4320=0"

"D=1044^2-4\\cdot360\\cdot4320=-5130864<0"

so, graphs R and C have not intersection points

q intercept of P are intersection points of graphs R and C


c)

break-even point is the point at which total revenue equals total costs or expenses

since graphs R and C have not intersection points, there are no break-even points


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