The manufacturing cost of an item consists ofRs900 as overheads. The material costs Rs3 per item and labor cost Rs x2/100 for x items produced. how many items must be produced to have minimum average cost?

Dear Student,

Let x items be produced
Total Cost of x items = 3xx2100 + 900
Average Cost (C) = 3x + x2100+900x = 3+x100+900x
dCdx = 1100-900x2

For maximum or minimum,    dCdx = 01100 - 900x2 = 0x2 = 90000x = 300



d2Cdx2 = 1800x3Now, d2Cdx2x=300 = 18003003 > 0 

So, 300 items should be produced to minimise the average cost.

Regards

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