Question

The manager of a furniture factory finds that it costs $2400 to manufacture 60 chairs in one day and $4800 to produce 260 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?
C) What is the y-intercept of the graph? What does it represent?

Answer 1

C(x) = 12x + 1680

Slope = 12

Intercept = 1680

Explanation:

Given that:

X1 = 60 chairs ; y1 = 2400

X2 = 260 chairs ; y2 = 4800

Obtain the slope ; m

m = y2 - y1 / x2 - x1

m = 4800 - 2400 / 260 - 60

m = 2400 / 200

m = 12

Using the point slope relation:

y - y1 = m(x - x1)

y - 2400 = 12(x - 60)

y - 2400 = 12x - 720

y = 12x - 720 + 2400

y = 12x + 1680

C(x) = 12x + 1680

From the general slope intercept equation :

y = mx + c

m = slope ; c = intercept

Hence,

C(x) = 12x + 1680

Slope = 12

Intercept = 1680