Differentiation

Profit for a monopolist`s product, the cost function is

c=0.004q^3(to the power 3) + 20q + 5000

and the demand function is

p=450 - 4q

Find the profit-maximizing output

Printable View

- Oct 13th 2008, 12:34 AMAndrew1380Urgent Calculus help needed?
Differentiation

Profit for a monopolist`s product, the cost function is

c=0.004q^3(to the power 3) + 20q + 5000

and the demand function is

p=450 - 4q

Find the profit-maximizing output - Oct 13th 2008, 12:52 AMbatman
profit is given by pq-c=(450 - 4q)q-0.004q^3 - 20q - 5000 = 0.004q^3-4q^2+430q-5000

Differentiate with respect to q and get

0.012q^2-8q+430.

Now set this equal to 0 and apply the quadratic formula,

q=(8-sqrt(8²-4*0.012*430))/(2*0.012) or q=(8+sqrt(8²-4*0.012*430))/(2*0.012).

The second isnt possible as there p<0, so your answer is q=(8-sqrt(8²-4*0.012*430))/(2*0.012) - Oct 13th 2008, 01:41 AMAndrew1380Thanks so much Batman!
Am doing self study and not so good with maths as am preparing for the pre-entry exam for the management finance, could you break it down in detail?(Happy)