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Homework answers / question archive / Final Exam Part II For the following exam portion show all of your thinking and mathematical processes to arrive at your answer
Final Exam Part II For the following exam portion show all of your thinking and mathematical processes to arrive at your answer. You must use the concepts in the course to demonstrate how you arrived at your answer. All work must be done individually without any assistance and by turning in this assignment under your D2L profile you are verifying that you alone did the work shown for this final exam and did not receive any help.
1. ????(????) = 2???? 2 + 3????
a. Using the definition of the derivative the find the derivative of ????(????)
b. Use basic differentiation properties to show your answer in part a is correct.
2. Let ???? = 480 − 0.8????, where ???? is the number of remote control cars that can be sold at a price of $???? per unit The manager of the store wants to know what price will maximize his revenue. He is currently charging $48 per car. Make a recommendation for the manager on what price to charge and explain your reasoning. Your reasoning should include:
a. Expressing the demand, ????, as a function of price, ????(????).
b. Determine if the demand is elastic at the current price by using methods taught in this course.
c. Find the revenue function ????(????)and include a graph in Geogebra or Desmos.
d. Make a recommendation to the manager where he should set the price to maximize his revenue. Write your answer as a complete sentence.
3. A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are ????(????) = 74,000 + 80???? and ????(????) = 300 − ???? 30 0 ≤ ???? ≤ 9000.
a. Find the revenue function and how many sets to produce for the maximum revenue.
b. Find the Profit function and find how many sets to produce for a maximum profit, as well as the price the company should charge for each television set that will realize this maximum profit.
A defense contractor is starting production on a new missile control system. On the basis of data collected during assembly of the first 16 control systems, the production manager obtained the function ???? ′ (????) = 1600???? − 1 2 for the rate of labor use. Approximately how many labor-hours will be required to assemble the 17th through 25th control units . (hint: Let a=16 and b=25)
