An important mathematical application in economics is to model the cost and revenue for a company. Net profit that the company earns is the value remaining after all operating expenses are subtracted from the revenue. Thus, Profit = Revenue - Cost, that is, P(x) = R(x) - C(x).

For this Discussion, suppose that for a certain company, the cost for producing items is 35x+30035x+300 and the revenue for selling items is 70x0.5x270x0.5x2.

Part a. What's the profit function,P(x) ?

Part b. Show work to find two values ofxthat will earn a profit of $200.

Part c. Is it possible for the company to earn a profit of $2,000? (Hint: What happen to the discriminant when P(x) = 2000? Will there be real solutions? Why or why not? Please show work! )