Assume that firm VYZ$\text{'}$s cost function is given by $C(q)=100+4q^2$ where $q$ is the level of output and $C$ is total cost. Please answer the following question in accordance.

If total revenue of the firm is simply the price multiplied by the quantity of output and the price of one unit of output is $40$ liras. Please write down the profit function for the firm and calculate the profit maximizing level of output $(10$pt$).($Hint: marginal revenue equals to marginal cost.$)$