The manager of a furniture factory finds that it costs $2200 to produce 100 chairs in one day and $5000 to produce 300 chairs in one day.

Question

1.

The manager of a furniture factory finds that it costs $2200 to produce 100 chairs in one day and $5000 to produce 300 chairs in one day.

(a) Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x chairs in one day.

Answer 1

C(x)= mx + b; we have two points: (100,2200) and (300,5000). So, slope m = (5000 - 2200)/(300 - 100) =

2800/200 = 14. Now we have C(x) = 14x + b. To get b: C(100) = 1400 + b = 2200, b = 2200 - 1400 = 800.

So, C(x) = 14x + 800. This is cost function