Help with a math problem...?

Question

The manager of a furniture factory finds that it costs $2800 to manufacture 80 chairs in one day and $4800 to produce 280 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.

C(x) =...

Answer 1

Let's convert these into coordinates to make it easier:

(80,2800)

(280,4800)

Now, find the slope:

SLOPE = (4800 - 2800) / (280 - 80)

SLOPE = 2000 / 200

SLOPE = 10

Now, use the slope formula again and use any point - I'm going to use (80,2800):

(y - 2800) / (x - 80) = 10

Cross multiply:

y - 2800 = 10(x - 80)

y - 2800 = 10x - 800

y = 10x + 2000

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Just change the y into C(x) to get the cost function:

C(x) = 10x + 2000