# quantitative analysis

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consider a manufacture whose total cost of producing x items is given by c(x) = 10000 + 5x+1/9x^2

a) what is the average cost function of A(x) = c(x)/x?
b)how many items should the manufacturer produce in order to minimize average cost?
c)what is the smallest average cost?
d) find c(x)
e) when does c(x) have a critical point? what is the average cost when c(x) has a critical point?

• quantitative analysis -

a(x) = c(x)/x = 10000/x + 5 + 1/9 x
da/dx = -1000/x^2 + 1/9
da/dx=0 when x = 30√10 = 94.868
a(94) = 121.8
a(95) = 120.8
so, it looks like the lowest average cost is at x=95

c(x) is a parabola whose vertex is at a negative x-value. So, there is no minimum cost.

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