Question

A manufacturer has daily costs given by the function C = 20,000 – 220x + 0.045x^2 where C is the cost and x is the number of units produced. How many units should be produced each day to yield the minimum cost for production?

Answer 1

Optimum is reached when the derivate equals zero
derivate of C is 2*0.045x-220 which is 0.09x-220
0.09x-220=0
x=220/0.09
x=2444,44 say 2445 units.