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Problem: Gazelle Corp, a sports shoe firm, is currently selling 800 pairs of a certain shoe per month. It is currently charging a price of £80, but this has recently been reduced from £90, because sales were only reaching 750 units per month. Its total costs are £56,000 per month, and these have risen £3000 due to the increase in sales.
Required:
Question 1: Derive the cost and demand functions for the firm, assuming these are both linear.
Question 2: Calculate the profit-maximizing price and output.
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