# Math Help - Differentiation - Calculus help!

1. ## Differentiation - Calculus help!

PROFIT for a monopolists product, the cost function is
c=0.004q^3 + 20q + 5000

and the demand function is
p=450 - 4q

Find the profit-maximizing output.

2. Originally Posted by Andrew1380
PROFIT for a monopolists product, the cost function is
c=0.004q^3 + 20q + 5000

and the demand function is
p=450 - 4q

Find the profit-maximizing output.

Revenue is:

$pq =450q -4q^2$

profit is revenue minus costs:

$pr(q)=450q -4q^2 - (0.004q^3 + 20q + 5000)=-0.004q^3-4q^2+430q-50000$

Now find the extrema of this by differentiating and setting the derivative to zero and solving for the critical values of q, the critical value that maximises the profit will be the profit maximising output.

q=50 and profit=6000
CB