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Question description

1. If the total cost of making x gallons of Exall is C(x) dollars where

C(x) = 100+3x+0.01x^2.

ind the expression for the marginal cost of the xth gallon, which is
C(x)−C(x−1).

(a) Find the marginal cost of the tenth gallon.

(c)Find the marginal cost of the ﬁftieth gallon.

d)Recall marginal cost is deﬁned using the derivatives as

MC(x) =dC(x) / dx.

Write the expression for the marginal cost in terms of the derivatives.
(e)Find the marginal cost of the tenth and ﬁftieth gallon using the derivative of the total cost function.

(f)Explain the difference in values you obtained using the two methods.
(g)Find the average cost of producing x gallons of Exall denoted by AC(x).
(h)Solve for the output x for which the marginal cost and the average cost are equal, i.e.,
AC(x) = MC(x).Denote this output as x^∗.
(i)Verify by drawing graph of the cost function AC(x) that the average cost attains it’s minimum at x^∗.

(Top Tutor) Daniel C.
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School: Purdue University
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