Differentiation - Calculus help!

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• Oct 12th 2008, 09:01 AM
Andrew1380
Differentiation - Calculus help!
PROFIT for a monopolist`s product, the cost function is
c=0.004q^3 + 20q + 5000

and the demand function is
p=450 - 4q

Find the profit-maximizing output.

Please assist step by step?(Worried)
• Oct 13th 2008, 05:31 AM
CaptainBlack
Quote:

Originally Posted by Andrew1380
PROFIT for a monopolist`s product, the cost function is
c=0.004q^3 + 20q + 5000

and the demand function is
p=450 - 4q

Find the profit-maximizing output.

Please assist step by step?(Worried)

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