Answer:
The manager of a furniture factory finds that it costs $2400 to manufacture 50 chairs in one day and $4800 to produce 250 chairs in one day.
(a) First we will find m, that represents the rate of change of cost with respect to number of chairs:
so, m = 12 dollars per chair.
Let C be the cost and X be the number of chairs, the function can be written as (assuming that it is linear):
![C-2400=12(x-50)](https://tex.z-dn.net/?f=C-2400%3D12%28x-50%29)
![C-2400=12x-600](https://tex.z-dn.net/?f=C-2400%3D12x-600)
![C=12x+1800](https://tex.z-dn.net/?f=C%3D12x%2B1800)
(b) Slope of the graph is m =12
Here slope represents that for every unit increase in number of chairs produced (X), the overall cost (C) will increase by 12 dollars.
Option - the cost (in dollars) of producing each additional chair.
(c) Y intercept is a dependent variable. It is $1800, when the value of independent variable (X) is 0. Also we can say that $1800 is the fixed cost that has to be paid irrespective of any chairs produced. If there is 0 production, still $1800 has to be paid.
Option - the cost (in dollars) of operating the factory daily.