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If a cost function is given by: C(x)=2x2+255x+5000C(x)=2x2+255x+5000, find the number of items for which average cost is at a minimum.

pur-new-sol

The average cost is the total cost divided by the number of units produced.

AC=2x2+255x+5000xAC=2x+255+5000x−1AC=2x2+255x+5000xAC=2x+255+5000x−1

To find the point where AC is minimized, we have to differentiate its function and then equate the derivative to zero.

AC=2x+255+5000x−1AC′=2−5000x−2AC=05000x−2=2x=50AC=2x+255+5000x−1AC′=2−5000x−2AC=05000x−2=2x=50

Thus, the average cost is minimized at 50 units.

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