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Homework answers / question archive / Suppose that c(x)=3x3−6x2+11,000xc(x)=3x3−6x2+11,000x is the cost of manufacturing xx items
Suppose that c(x)=3x3−6x2+11,000xc(x)=3x3−6x2+11,000x is the cost of manufacturing xx items.
Find a production level that will minimize the average cost of making xx items.
The production level that minimizes the average cost of making xx items is x=x= _____ .
The given cost function is:
c(x)=3x3−6x2+11000xc(x)=3x3−6x2+11000x
Finding the average cost function by using the formula:
A(x)=c(x)xA(x)=3x3−6x2+11000xxA(x)=3x2−6x+11000A(x)=c(x)xA(x)=3x3−6x2+11000xxA(x)=3x2−6x+11000
Finding the derivative of A(x) with respect to x, we get:
A′(x)=6x−6A′(x)=6x−6
Putting A'(x) = 0, we get:
6x−6=0x=16x−6=0x=1
Finding the second derivative of A(x), we get:
A′′(x)=6>0A″(x)=6>0
Implies that, A(x) is minimum at x = 6.
The production level that minimizes the average cost of making xx items is x=6x=6.
