profit maximisation using calculous

Q1. The demand and cost functions of a monopolist are p=100-3q+4A^1^/^2 and C=4q^2+10q+A(A is the level of advertising expenditure). Find the values of A,q and p that maximise profit.

Since here, profit is a function of q and A, I want to find the value of q and A at maximum profit, by using "total derivative". Will that be correct?

Re: profit maximisation using calculous

Firm will maximize profits (pi)

pi=pq-C

max (100-3q+4A^(1/2))q-(4q^2+10q+A)

Take the first order conditions with respect to A, q,p (i.e partial derivative w/ respect to each set to zero)

next make sure second order condition is satisified.

Then solve for the A,q,p that maximize profits. Hope this helps

Re: profit maximisation using calculous

Thank you so much!(Happy)