If the total cost of producing X units of a product is given by C(X)= 10,000 + 20xe X/600... find the marginal cost when 600 units are produced
C(X)= 10,000 + 20xeX/600
makes no sense to me, did you mean
C(X)= 10,000 + 20xe^(x/600) ??
if so, just plug in x = 600
to get C(600) = 10000 + 600(e^1)
= ....
e^1 = 2.718281828...
To find the marginal cost when 600 units are produced, we need to calculate the derivative of the cost function C(X) with respect to X and then evaluate it at X = 600.
The cost function is given by C(X) = 10,000 + 20xe^(X/600).
To find the derivative, we'll need to apply the product rule and the chain rule. Let's start by differentiating the cost function term by term.
The derivative of 10,000 is 0 because it is a constant.
To differentiate 20xe^(X/600), first, differentiate the term 20x with respect to x, which gives 20. Then differentiate e^(X/600) with respect to X, which gives (1/600)e^(X/600).
So, the derivative of the cost function C(X) is:
C'(X) = 20 + (1/600)e^(X/600)
Now, we can evaluate the derivative at X = 600 to find the marginal cost.
C'(600) = 20 + (1/600)e^(600/600)
= 20 + (1/600)e^1
= 20 + (1/600)e
Therefore, the marginal cost when 600 units are produced is 20 + (1/600)e.