The average cost of producing x units of a commodity is given by the equation
c(x) = 20.4 - 0.0007x. Find the marginal cost at a production level of 1255 units. Round to two decimal places.
It is my understanding that to figure out marginal cost, you take the derivative of c(x) and substitute 1255, correct? Well, differentiating in this case takes away all of the x's.....so I am completely lost. Is there no marginal cost?
Strictly speaking, the "marginal cost" is the cost to produce "one more". For complicated functions, that is difficult to calculate and can be approximated by the derivative- and depends upon how many are being produced.
For a linear function, however, that is easy. If c(x)= 20.4 - 0.0007x, then c(x+ 1)= 20.4- 0.0007(x+ 1)= 20.4- 0.007x- 0.0007. Here, the cost of producing x+ 1 is -0.007, 0.0007 less than producing x. The marginal cost is -0.0007 no matter what x is.
Or, in terms of the derivative, yes, the derivative is c'(x)= -0.0007, a constant function. But that just means that c(1255)= -0.0007- the marginal cost is -0.0007.
You might want to check your problem again- costing less to produce more is a bit unusual!
Can't argue with that! That's why I wanted to double check everything. It does not seem remotely correct to me, but that's how the problem is written exactly.