ECON 3205 - Two plants (factories) in Mexico that manufacture shoes

You are the manager of two plants (factories) in Mexico that manufacture shoes. The combined monthly output of both plants is to be 10,000 pairs of shoes. Explain, based on your understanding of Chapter 7 (The Cost of Production), how you would best divide this output of 10,000 pairs of shoes between the two plants. You may make your arguments in words with the aid of diagrams, i.e., without the use of math. On the other hand, if you are comfortable with math (calculus), the following additional information may be made use of by you. The cost function of Plant 1 is C₁= a₁Q₁ + a₂Q₁² + Q₁³ and that of Plant 2 is C₂ = b₁Q₂ + b₂Q₂² + Q₂³, where Q₁ and Q₂ denote, respectively, the outputs of Plant 1 and Plant 2.