1. (20 points) A company is planning to manufacturing and market a new electric pens. After conducting market survey, the research department estimates that a price of $16 will result in a weekly demand of 200 pens and that a price of $14 will result in a weekly demand of 300 pens. The financial department estimates that weekly fixed costs for this item will be $1,400 and that the cost of producing each pen will be $4. Evaluate the following: 1. Find the price demand equation. Assume it is linear. 2. Determine the domain on the product x in the part (1). 3. Sketch the price equation. 4. Find the total cost function. Find the marginal cost function. 5. Find the revenue function R(x). 6. Find the profit function. 7. Evaluate: R(x), and R(x) for each of the following: x=200,450, and 800 . Then interpret the results. 8. Sketch the Cost and Revenue function in the same plane. Then describe the domain of loss, profit, and find Break-even points