Suppose that a firm can sell a quantity q at a price of 10 q. The firm's costs are given by C(q) = q 3 + F for some F > 0. The constant F is a fixed cost that only needs to be paid if the firm opens its doors (think of this as registering the firm, buying land for production, etc.). If the firm does not open its doors, it earns 0 profits. a) (6 marks) Suppose that the firm has chosen to open its doors. What is the level of q which maximizes profits? b) (6 marks) For what values of F should the firm open its doors