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?
Revenue is:
$\displaystyle pq =450q -4q^2$
profit is revenue minus costs:
$\displaystyle pr(q)=450q -4q^2 - (0.004q^3 + 20q + 5000)=-0.004q^3-4q^2+430q-50000$
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