This is a calculus question..please help!?

Question

Afurniture company finds that it costs $2200 to make 100 chairs in one day and $4800 to make 300 chairs in one day.

A. express the cost as a funtion of the number of chairs produced, assuming that it is linear.

B. what is the slope and what does it represent?

C. what is the y intercept and what does it represent?

is this a piecewise graph??

Answer 1

y = (4800-2200)/ 300-100 = 13x +b
2200 = 13*100 +b so b = 900
The equation is y = 13x +900 where y is the cost and x is the number of chairs

The slope is 13 and represents the incremeantal cost per chair. The y-intercept is $900 and represents startup costs.

No. This is a straight line.

Answer 2

Let "y" be the dependent variable (which is the cost) depending upon the no. of chairs "x" that is the independent variable.

We assume a linear relation between "x" and "y", i.e
y=mx+c, where "m" is the slope and "c" is the y-intercept.
Then

2200 =m*100 +c (i)
4800=m*300 +c (ii)

Subtracting (i) from (ii) we get
2600 = m*200 or m=2600/200=13

Substituting this value of m in (i) we get
2200=1300+c or c=2200-1300 = 900

Hence the linear relation between the cost and the number of chairs becomes
y=13x+900 [This answers A]

The slope is 13, This is the cost incurred for making each chair. [This answers B]

The y-intercept is 900. This is the fixed cost in running the factory even if a single chair is not made. [This answers C]

This is not a piecewise graph. This is a continuous graph.

Answer 3

a - y = 900 + 13x

b - the slope is the cost per chair in production

c - the y intercept is the cost to set up the operation