A company manufactures two products. If it charges price p i for product i, it can sell q i units of product i, where q 1 = 60 - 3p 1 + p 2 and q 2 = 80 - 2p 2 + p 1 . It costs $25 to produce a unit...

A company manufactures two products. If it charges price p_i
for product i, it can sell q_i
units of product i, where q₁
= 60 - 3p₁
+ p₂
and q₂
= 80 - 2p₂
+ p₁. It costs $25 to produce a unit of product 1 and $72 to produce a unit of product 2. How many units of each product should the company produce, and what prices should it charge, to maximize its profit?