Gazelle Corp, a sports shoe firm, is currently selling 800 pairs of a certain shoe per month. It is currently charging a price of %40, but this has recently been reduced from $45, because sales were only reaching 750 units per month. Its total cost are $28,000 per month, and these have risen $1500 due to increase in sales.

Derive the cost and demand functions for the firm, assuming these are both linear?

Calculate the price elasticity of demand at the current price?

Comment on the firms existing strategy in terms of profit maximization, without doing any calculations?

calculate the profit-maximizing price and output?

Calculate the amount of profit that the firm is currently foregoing ?