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Problem: Christopher decides to produce a new blue colored cola, Sky, designed to compete with the major brands of Coke and Pepsi. Analysts have determined that the demand curve for Sky cola is P = 102 - 2Q, where P is the price and Q is the quantity(in crates) of cola. The total cost for producing the cola is given by TC = 700 + 2Q + 0.5Q2
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Question 1: Christopher's company is currently producing 15 crates of Sky cola per day and selling them for $57.50 per crate. Antonio, the company auditor, wants to know if it is maximizing profits. Is it? Explain and provide mathematical proof.
Question 2: How much excess capacity is Sky working with?
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