Question

In the assortment of the small computer equipment company Computer-XY you will find a selection of different computer mice.
The production cost of TSK, which is the best seller for the company, can be modeled as follows:
C (x) = 0.02x^2 + 80x + 800
a) Find the unit cost function. A(x)
b) Determine the asymptotes of A by calculation.
c) Discuss the monotony properties of the unit cost function at the interval [0,1) when calculating.
For which number of units produced is the unit cost the least?

Answer 1

C(x)=0.02x2+80x+800

a) Unit cost functionA(x)=800—80x+0.02*2

(0.02)x²—80x+800

X=—b/2a. X=—(—80)/2(0.02)=80/0.04=2000

b)asymptotes of A

Line A is a horizontal asymptotes of function

A=f(x),if either.

lim_x›infinity2000=2000

lim_x—infinity2000=2000. Thus the horizontal asymptotes is A=2000

c) eg:if y=g(x)is strictly monotonic on the range [0,1],then it has an inverse x=h(y) on the range [g(0),g(1)]entire range of the function has an inverse.

Companies seek to maximize profit by reducing unit costs and optimizing the market offering price.