2. A company has determined that the demand for its security systems can be shown by the demand equation p = 1160-4q, where p is the price per system and q is the number of systems made and sold in 100's. The total cost of producing q number of security systems is C(q) = 120q + 42000. a. Find the number of security systems the company needs to sell in order to maximize profit. (8 points) b. Find the maximum profit. (3 points) c. Find the optimal price that will allow the firm to maximize profits. (2 points)