The manufacturing cost of an item consists ofRs900 as overheads The material costs Rs3 per item and labor cost - Maths - Application of Derivatives

Question

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?

Mayur Pisode · Accepted Answer

Dear Student,

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

For maximum or minimum,    dCdx = 0⇒1100 - 900x2 = 0⇒x2 = 90000⇒x = 300

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

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

Regards

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?

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?