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