Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 16

It will cost $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day according to the manager of a furniture factory.



a.) Express the cost as a function of the number of chairs produced, assuming that it is linear then sketch its graph.



$\begin{equation} \begin{aligned} c &= ax + l \text{ where}:\\ c &= \text{cost}\\ a &= \text{slope}\\ x &= \text{number of chairs}\\ k &= \text{other expenses} \end{aligned} \end{equation}$


Given:

$\text{when } \begin{array}{llllll} x &=& 100 &c &=& 2200\\ x &=& 300 &c &=& 4800\\ \end{array}$


Substituting these values to the equation will result to :



$\begin{equation} \begin{aligned} a &= 13\\ k &= 900 \end{aligned} \end{equation}\\ \boxed{.: c= 13x+900}$





b.) Find the slope of the graph then state what does it represent.

The slope is 13, it represents the change in cost for every change in the number of chairs.

c.) Find the y-intercept of the graph and state what does it represent.

The $y$ intercept is 900, maybe it represents the charges for the maintenance of the equipment used.