A Firm Produces Two Products (A and B) Jointly $$Q _ { A } = 3000 - 20 P _ { A } \quad Q _ { B } = 1000 - 10 P _ { B }$$

Essay

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: $$Q _ { A } = 3000 - 20 P _ { A } \quad Q _ { B } = 1000 - 10 P _ { B }$$ 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: $$\text { (i) } M C = 70 + 0.30 Q$$ $$\text { (ii) } M C = 10 + 0.04 Q$$