SOLUTION: In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projecti

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Question 44895: In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
Answer by Chris435435(8) (Show Source):
You can put this solution on YOUR website!
The problem tells you that there is a linear relationship between the variables C and x. So we have some information about the relationship between the variables. That is:

Using this relationship and the other information in the problem, we can solve this problem. We know that the cost should be 10000 when the number of items produced is 100. That is:

We also know that the cost should be 22000 when the number of items produced is 300. We know two pieces of information that must be satisfied for the relationship to hold. That is:

This is a system of equations that you can solve now. Solving these equations I get m = 60 and b = 4000.
So our relationship between C and x is

Let's check to make sure that this is legitimate by checking what it should satisfy. C should equal 10000 when x = 100.

Also, C should equal 22000 when x = 300.

Therefore, the relationship is valid and our question is answered.