Choose ONE problem. Answer the problem questions using a complete sentence incorporating the language and context of each problem as appropriate. Show all the steps using proper notation to complete these problems as were presented in class. That means show first and second derivative tests as appropriate. Show your work when forming equations. Make sure your work is neat, answers are legible, problem is neatly presented free of scratch outs. Outline the steps you took to complete the signature assignment.

After you have competed the signature assignment problem, you will respond to the following prompts and write a reflection (5-10 sentences) utilizing the Signature Assignment Prompts to summarize the assignment.

Save the completed assignment as 150YourLastName and submit in the folder in the ‘Integrative Writing’ module on blackboard.

Signature Assignment Reflection Prompts

1. What impact did the Signature Assignment have on your understanding of calculus?

2. What new knowledge did you gain about your calculus topic? Briefly explain. 

3. What did you learn by creating the signature assignment?

4. What challenges did you face completing the assignment?

5. How will calculus be useful to you in the real world?

Problems: (Choose one)

1. The price-demand equation for a GPS device is where is the demand and is the price in dollars.

A. Find the production level that produces the maximum revenue.

B. Find the price per unit that produces the maximum revenue.

C. What is the maximum revenue?

D. If the GPS device cost the store $220 each, find the price to the nearest cent that maximizes the profit.

E. What is the maximum profit to the nearest dollar?

G. Write the signature assignment reflection using the assignment prompts.

2. At a price of $8 per ticket, a musical theatre group can fill every seat in the theatre, which has a capacity of 1500. For every additional dollar charged, the number of people buying tickets decreases by 75.

A. What ticket price maximizes revenue?

B. What is the maximum revenue?

C. Briefly summarize your findings so anyone could understand your answer to the problem.

D. Write a signature assignment reflection using the assignment prompts.

3. The concentration of a drug in the blood stream , in milligrams per cubic meter any time , in minutes is described by the equation

Where corresponds to the time at which the drug was swallowed.

A. Determine how long it takes the drug to reach its maximum concentration.

B. What is the maximum concentration?

C. Briefly summarize your findings so anyone could understand your answer to the problem.

D. Write a signature assignment reflection using the assignment prompts.

4. A motel finds that it can rent 200 rooms per day if it charges $80 per room. For each $2 increase in rental rate, two fewer rooms will be rented per day.

A. If each rented room costs $8 to service per day, how much should the management charge for each room to maximize gross profit?

B. What is the maximum gross profit?

C. Briefly summarize your findings so anyone could understand your answer to the problem.

D. Write a signature assignment reflection using the assignment prompts.

5. Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be

It also determines that the total cost of producing x suits is given by

A. Find the maximum revenue.

B. How many suits must be sold to maximize revenue?

C. How many suits must the company produce and sell in order to maximize profit?

D. Find the maximum profit.

E. What price per suit must be charged in order to maximize profit?

F. If the government decides to tax the company the $10 for each suit it produces, how many suits should the company produce to maximize its profit? What is the maximum profit with the government tax? How much should the company charge for each suit?

G. Briefly summarize your findings so anyone could understand your answer to the problem.

H. Write a signature assignment reflection using the assignment prompts.