A manager of two plants (factories) in Mexico manufacture shoes. The combined monthly output of both plants is to be 10,000 pairs of shoes. how would the manager best divide this output of 10,000 pairs of shoes between the two plants. The following information may be made of use. The cost function of Plant 1 is C₁ = a₀ + a₁Q₁ + a₂Q₁² + a₃Q₁³ and that of Plant 2 is C₂ = b₀ + b₁Q₂ + b₂Q₂² + b₃Q₂³, where Q₁ and Q₂ denote, respectively, the outputs of Plant 1 and Plant 2.