A company has a monthly production function of f(x)=−x3+24x2+12x where x is the average number of employees working per shift. Where is the point of diminishing returns?

Answer 1

f'(x) = -3x^2 + 48x + 12 = 0

x^2 - 16x - 4 = 0

x= 16/2 + or - (1/2)sqr(16^2 +16)

x = 8 + or - 8.25 = 16.25

with the 17th worker, production goes down

f(16) = -16^3 + 24(16)^2 + 12(16) = 2240

f(17) = -17^3 + 24(17^2 + 12(17) = 2227

production diminishes by 13 with the 17h worker. marginal productivity is negative. workers are getting in each others' way.