You just started as an intern at a new company and your first task is to help them price a product that they are about to deploy. After running an experiment, you estimate that the daily demand for your new product is equal to D(p)=180-p. The cost of producing one unit of this product is $25. You can assume 365 days in a year. a. Your manager who didn't take 311 insists on setting the price so that costs are covered plus a target profit margin of 15%. How much is the annual profit based on your manager's pricing strategy? b. After taking 311 you can propose an alternative price for the new product. What is the optimal price? c. What is the annual production cost based on the price that you recommended in part (b)? d. How much did the company's annual profits increase due to your proposed strategy? e. Now that you are well established in the company, you bring up the possibility of doing price differentiation and charging two different prices. Your manager steals your idea and pitches the following two prices to the board: a low price of $100 and a high price of $180. Assuming you can successfully implement price differentiation, what is the annual profit if the company goes with your manager's recommendation? f. After your manager's choices for prices failed, the board gives you some flexibility to choose any high price you want, but insists on leaving the low price at $100. What is the optimal high price that maximizes profit? Please justify numerically for full credit.