A Firm Produces Two Products (A and B) Jointly $$Q _ { A } = 400 - 4 P _ { A } \quad Q _ { B } = 100 - 2 P _ { B }$$

A firm produces two products (A and B) jointly. Every time a unit of A is produced, a unit of B is also produced as a byproduct. The demand functions for A and B are: $$Q _ { A } = 400 - 4 P _ { A } \quad Q _ { B } = 100 - 2 P _ { B }$$ Assuming that disposal is costless, determine the number of units of A and B that the firm should produce, the number of units of A and B that the firm should sell, and the price that should be charged for each of the products if the firm's marginal cost of producing a unit of joint output is: $$\text { (i) } M C = 100 + Q$$ $$\text { (ii) } M C = 0.125 Q$$