Question: A firm manufactures a commodity at two different factories. The total cost of manufacturing depends on the quantities, q 1 and q 2 , supplied

A firm manufactures a commodity at two different factories. The total cost of manufacturing depends on the quantities, q₁ and q₂, supplied by each factory, and is expressed by the joint cost function,

C = f(q₁, q₂) = 2q²₁ + q₁q₂ + q²₂ + 500.

The company’s objective is to produce 200 units, while minimizing production costs. How many units should be supplied by each factory?

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