The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.

Question

The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800

to produce 300 chairs in one day.

(a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the

graph.

(b) What is the slope of the graph and what does it represent?

(c) What is the y-intercept of the graph and what does it represent?

Answer 1

To be linear, y = mx+b

300m + b = 4800

100m + b = 2200

Subtracting the two equations, 200m = 2600

m = 13

13(100)+b = 2200

b = 2200-1300 = 900

a) Cost, C(x) = 13x+900

To sketch the graph, put a point at (0,900) and points at (100,2200) and (300,4800) and draw a line

through those points.

b)The slope is 13. This is the cost per chair produced.

c)The y-intercept is 900. This is the overhead cost to run the factory.