Question

A manufacturer has

determined that m employees will produce a total of q units of

product per day, where

q = m(60 − m)

If the demand function is given by

p = −0.02q + 12

fifind the marginal-revenue product when m = 10.

Answer 1

marginal revenue equation is the first derivative of the revenue function.

revenue function is given by $F \times Q$

$F=-0.002q +12$

$R=F \times q$

$R=( -0.002q + 12) \times q$

$R=-0.002q^2+12q$

But marginal revenue is given by the first derivative of the revenue function

$MR=\frac {\Delta R}{\Delta q} 0.002q^2+12q$

$MR=-0.004q+12$

but $q$ is given by $q = m(60 − m)$

when $m=10$

$q=10(60-10)$

$q=600-100$

$q=500$

$MR=(-0.004 \times 500)+12$

$MR=-2 +12$

$MR=10$

MARGINAL REVENUE = $10units$