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.
a) Derive the cost and demand functions for the firm, assuming these are both linear.
b) Calculate the profit-maximizing price and output.