A company manufacturing widgets has a fixed cost of $5,000, and a variable cost of $3 per widget. Suppose that the demand equation for widgets is given by q = 500 - 50p, where p is the price in dollars of one widget, and q is the number of widgets that can be sold at price p. 1. Write the function C(p), total cost, when the price is set at p
2. Write the function R(p),revenue, when the price is set at p
3. Write the function (p), profit, when the price is set at p
4. Find a function for the marginal profit for these widgets