P=100-30+4a½

Tc=4q²+10q+a
find q,p,a values

answr

10q

11423

.

114484

To find the values of q, p, and a, we need additional information or equations that relate these variables. The given equations P = 100 - 30 + 4a½ and Tc = 4q² + 10q + a only provide relations between variables, but not enough information to solve for a unique solution.

Please provide more information or equations with known values so that we can solve for q, p, and a.

I think this is what you want:

A firm with monopoly power has the demand curve: P = 100 - 3Q + 4A^1/2
And has the total cost function: C = 4Q^2 + 10Q + A where A is the level of advertising expenditures.
P is price, Q is output. How do I find the values of A, Q, …

You will get a family of curves. I would do this:
from P, a=(P/4-7.5q)^2 and square that out.
then insert the quadratic into the Tc equation for a, and combine like terms.

You will have a function tc dependent on P and q. You can then plot that family, or use your analytical methods to maximize profit, if you have a profit function. With what you have given, demand, and cost, there is no profit function.