Calculus cost problem?!?

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.

I just have no idea....

i really dont care about the answer...i just want someone to show me the steps/reasoning to get to the answer

thanks

Answer 1

ok so if you check, the cost of production doubles while the chair production multiplies by five. so the equation will probably involve fifths or half's and the relationship between how many times something is multiplied when the other variable changes. Well, there's your math lingo.  Good luck.

Answer 2

c(x) = 12x + 1800

How to get this:

The slope of a line is , for 2 data points, the difference in the y-values

over the difference in the x values.

Here, 4800 - 2400 = 2400

  and    250 - 50   =  200

Divide them for the slope:  2400 / 200 = 12

Now y = 12x + b

Substiute one data point to find b:

use (50,2400)    2400 = 12(50) + b

                            b =  1800

So C(x) = 12x + 1800

ANSWER

Answer 3

your solution needs to be in the form y = mx + b. You know this because the problems states "assume that it is linear".

y is going to be the cost of the product so that'll be C

m is the slope of the graph and we can derive this by doing rise over run or (4800 - 2400) / (250 - 50) = 2400 / 200 = 12

x is going to be chairs produced.

So now we have : C = 12X + b. So all that's left is to solve for b.

To get b, we'll plug and chug one of the data points given to us, let's use (50, 2400)

So: 2400 = 12 * 50 + b

Solve for b: b = 1800

So your final answer is C = 12 x + 1800

Hope it helps