Word Problems with Quadratic Inequalities

In economics a company's profit can be expressed as its total revenue minus it's total cost (expressed as $\Pi=TR-TC$). (Note: in economics they use the pi symbol for profit, this isn't actually the number pi.)

Total revenue is the product of the price the good is sold at and the quantity of the good you produce (expressed as $TR=p\cdot q$). Finally, total cost is the sum of variable cost and fixed cost. Variable cost is the cost to produce the good multiplied by the quantity you make. Fixed cost is a set cost that does not rely on the quantity made (expressed as $TC=c\cdot q+FC$).