Question

suppose that c(x)=3x^3-12x^2+9000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Answer 1

c(x)=3x²(3)-12x²(2)+9000x
c(x)=9x²-24x+9000
9x²(2)-24x+9000=0
This can be factored to 3(3x²-8x+3000)
By not producing anything we constantly escalate our cost, there is no value for x.
By using a rational expression x=4/3+i√2246/3 and x=4/3-i √2246/3