A company manufactures two products. If it charges price p1 for product 1 and price p2 for product 2, it can sell quantities q1 = 55 − 3p1 + 2p2 and q2 = 75 + 2p1 − 2p2 for products 1 and 2, respectively. It costs the company $20 to produce a unit of product 1 and $65 to produce a unit of product 2. a. How many units of each product should the company produce? What prices should it charge, to maximize profit? b. Suppose the company must produce a minimum of 20 units of each product. How many units of each product should the company produce in that case? What prices should it charge, to maximize profit?