Suggested languages for you:

Americas

Europe

Problem 10

The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula $$ C(x)=100+40 x-0.001 x^{2} $$ a. Find the marginal cost function and use it to estimate how fast the cost is going up at a production level of 100 teddy bears. Compare this with the exact cost of producing the 101st teddy bear. HINT [See Example 1.] b. Find the average cost function \(\bar{C}\), and evaluate \(\bar{C}(100)\). What does the answer tell you? HINT [See Example 4.]

Expert verified

The marginal cost of producing 100 teddy bears is approximately \(39.80, the exact cost of producing the 101st teddy bear is $40.01, and the average cost of producing 100 teddy bears is $38.20. The average cost tells us the cost per teddy bear at a production level of 100 teddy bears.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 11

Dorothy Wagner is currently selling 20 "I \(\mathcal{Q}\) Calculus" T-shirts per day, but sales are dropping at a rate of 3 per day. She is currently charging \(\$ 7\) per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by \(\$ 1\) per day. How fast, and in what direction is her daily revenue currently changing?

Chapter 11

The weekly revenue from the sale of rubies at Royal Ruby Retailers (RRR) is increasing at a rate of \(\$ 40\) per \(\$ 1\) increase in price, and the price is decreasing at a rate of \(\$ 0.75\) per additional ruby sold. What is the marginal revenue? (Be sure to state the units of measurement.) Interpret the result. HINT [See Example 5.]

Chapter 11

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(f(x)=(4 x-1)^{-1}\)

Chapter 11

Marginal Product Paramount Electronics has an annual profit given by $$ P=-100,000+5,000 q-0.25 q^{2} $$ where \(q\) is the number of laptop computers it sells each year. The number of laptop computers it can make and sell each year depends on the number \(n\) of electrical engineers Paramount employs, according to the equation $$ q=30 n+0.01 n^{2} $$ Use the chain rule to find \(\left.\frac{d P}{d n}\right|_{n=10}\) and interpret the result.

Chapter 11

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(f(x)=\left[(3 x-1)^{2}+(1-x)^{5}\right]^{2}\)

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner