In this assignment, you will use what you have learned about derivatives to solve a problem about economics. When you are finished. take a picture or scan your work, and upload it to this assignment for grading. An electronics manufacturer is planning on introducing a new wireless microphone for use with laptops and mobile phones. The manufacturer has done some market research and concluded that if they set the sale price atp dollars per item, they can expect to sellN = 5000 10192 microphones per month. It costs $3.000 to each month to keep the factory open, and an additional $10 dollars to manufacture each microphone. The manufacturer needs to determine what price they should sell the microphones at in order to maximize their overall profit. Answer the following questions to help them determine what sale price they should use. 1. Write a formula for the total cost of production, 0, in terms of N. the number of microphones manufactured. 2. Use your answer to (1) to write a formula for the total cost of production, 0, in terms of p, the sale price. 3. Write a formula for the total revenue, R, in terms of p. 4. Combine your answers from {3) and (4) to write a formula for the profit in terms of p. Using a graphing calculator of utility such as Desmos, graph your function from {4). and observe that it has a maximum value at a point where the tangent line would be horizontal in other words, at a place where the derivative would be 0. Then continue with the questions below. . Compute the derivative of your answer from (4) . Set the derivative equal to 0 and solve for 33. What price should the manufacturer sell the microphones at? . If the manufacturer sets the price equal to the value you found in {6), how many microphones should they expect to sell each month? (Keep in mind that they can't sell part of a microphone.) . If the manufacturer sets the price equal to the value you found in {6), how much revenue should they expect to bring in each month? . If the manufacturer manufactures the number of microphones you found in (7), what would be their monthly production costs? 10. If the manufacturer sets the price equal to the value you found in {6), how much profit should they expect to earn each month