Question

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) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.
(b) What is the slope of the graph? What does it represent? the cost (in dollars) of producing each additional chair the number of chairs produced the cost (in dollars) of operating the factory daily the time (in days) to produce each additional chair
(c) What is the y-intercept of the graph? What does it represent? the cost (in dollars) of producing each additional chair the cost (in dollars) of operating the factory daily the time (in days) to produce each additional chair the number of chairs produced

Answer 1

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:

$\frac{4800-2400}{250-50}= 12$ 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):

$C-2400=12(x-50)$

$C-2400=12x-600$

$C=12x+1800$

(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.