For a certain company, the cost for producing x items is 55x+300 and the revenue for selling x items is 95x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

Part b: Find two values of x that will create a profit of $300.

Part c: Is it possible for the company to make a profit of $15,000?