A company operates two plants which manufacture the same item and whose total cost functions are C1=8.5+0.02q(subscript 1)^2 and C2=4.8+0.04q(subscript 2) ^2 where q1 and q2 are the quantities produced by each plant. The total quantity demanded, q=q(subscript 1)+q(subscript 2) , is related to the price, p , by p=50−0.04q. How much should each plant produce in order to maximize the company's profit?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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A company operates two plants which manufacture the same item and whose total cost functions are C1=8.5+0.02q(subscript 1)^2 and C2=4.8+0.04q(subscript 2) ^2 where q1 and q2 are the quantities produced by each plant. The total quantity demanded, q=q(subscript 1)+q(subscript 2) , is related to the price, p , by p=50−0.04q. How much should each plant produce in order to maximize the company's profit?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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