(Solution) - The Bergen Company and the Gutenberg Company are the only -(2025 Original AI-Free Solution)

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The Bergen Company and the Gutenberg Company are the only two firms that produce and sell a particular kind of machinery. The demand curve for their product is
P = 580 - 3Q
where P is the price (in dollars) of the product, and Q is the total amount demanded. The total cost function of the Bergen Company is
TCB = 410QB
where TCB is its total cost (in dollars) and QB is its output. The total cost function of the Gutenberg Company is
TCG = 460QG
where TCG is its total cost (in dollars) and QG is its output.
a. If these two firms collude and they want to maximize their combined profit, how much will the Bergen Company produce?
b. How much will the Gutenberg Company produce?
c. Will the Gutenberg Company agree to such an arrangement? Why or why not?