If the marginal cost of producing x units of a commodity is given by C'(x)= 0.3x^2+2x and fixed costs are $2000. Find c(x) and the cost of producing 20 units.
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To find c(x) we need to antidifferentiate C'(x)= 0.3x^2+2x. When we do we get:
c(x) = 0.1x^3 + x^2 + k, where k is a constant
We know that k = 2000 because we are told $2000 is the fixed cost. We now have the cost function:
c(x) = 0.1x^3 + x^2 + 2000
The cost of producing 20 units is:
c(20) = $3,200
c(x) = 0.1x^3 + x^2 + k, where k is a constant
We know that k = 2000 because we are told $2000 is the fixed cost. We now have the cost function:
c(x) = 0.1x^3 + x^2 + 2000
The cost of producing 20 units is:
c(20) = $3,200
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