The cost of manufacturing of certain items consists of INR1600 as overheads, INR30 per item as cost of material and the labour costs INR x2100 for x items produced . how many items must be produced to have a minimum average cost ?
Let the number of units produced is x.
Overhead cost =Rs.1600
Material cost =30x
Labor cost =x2100
Total cost =1600+30x+x2100
Divide by x to get average cost.
Average cost
=1600x+30+x100Now to minimize differentiate and equate to 0.
0=−1600x2+1100
∴ 1600x2=1100
∴ x2=160000
∴ x=400