Question

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.

Answer 1

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