The cost in dollars of producing X pounds of a chemical in a factory is given by C(X). Suppose that the "marginal cost" is C'(X)= -.05 + .001x $/pounds.
A. It cost $12,150 extra to increase production from 500 pounds to 5000 pounds.
B. Suppose the cost of producing 0 pounds of the chemical is $5000. (You need to pay rent even if you close down production)
Find the function of C(X).
+130511 If C'x = -.05 + .001x.......then the variable cost part of the function becomes :
-.05x + .0005x^2
And the fixed cost part of the function is just 5000
So.....the function is :
C(x) = -.05x + .0005x^2 + 5000
Proof :
Note that the cost to produce 500 lbs is
C(500) = $5100
And the cost to produce 5000 lbs is
C(5000) = $17250
So....the extra cost to increase production from 500 to 5000 lbs = $[17250 - 5100] = $12150
