Concept explainers
Profit The monthly profit P for a widget producer is a function of the number n of widgets sold. The formula is
Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is vallid up to a level of 15 thousand widgets sold.
a. Make a graph of P versus n.
b. Calculate P(1) and explain in practical terms what your answer means.
c. Is the graph concave up or concave down? Explain in practical terms what this means.
d. The break-even point is the sales level at which the profit is 0. Find the break-even point for this widget producer.
Trending nowThis is a popular solution!
Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Glencoe Algebra 2 Student Edition C2014
Algebra and Trigonometry (6th Edition)
College Algebra: Graphs and Models (6th Edition)
Intermediate Algebra (12th Edition)
- Profit The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is P=2+2.9n0.3n2 Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 7 thousands widgets sold. a.Make a graph of P versus n. b.Calculate P0 and explain in practical terms what your answer means. c.At what sales level is the profit as large as possible?arrow_forwardHOW DO YOU SEE IT? The cost C for a business to make personalized T-shirts is given by Cx=7.50x+1500 where x represents the number of T-shirts. The graphs of C and C1 are shown below. Match each function with its graph. Explain what C(x) and C1(x) represent in the context of the problem.arrow_forwardRecycling The cost C (in dollars) of supplying recycling bins to p of the population of a rural township is given by C=25,000p100p,0p100. (a) Use a graphing utility to graph the cost function. (b) Find the costs of supplying bins to 15,50,and90 of the population. (c) According to the model, is it possible to supply bins to 100 of the population? Explain.arrow_forward
- Business The annual cost C (in thousands of dollars)and revenue R (in thousands of dollars) for a company each year from 2010 through 2016 can be approximated by the models C=2549t+1.1t2 and R=341+3.2t where t is the year, with t=10 corresponding to 2010. (a) Write a function P that represents the annual profit of the company. (b) Use a graphing utility to graph C, R, and P in the same viewing window.arrow_forwardRevenue The table shows the monthly revenue y (in thousands of dollars) of a landscaping business for each month of the year 2016, with x=1 representing January. A mathematical model that represents these data is fx1.97x+26.30.505x21.47x+6.3. (a) Use a graphing utility to graph the model. What is the domain of each part of the piecewise-defined function? How can you tell? (b) Find f5 and f11 and interpret your results in the context of the problem. (c) How do the values obtained from the model in part b compare with the actual data values?arrow_forwardBusiness The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each year from 2010 through 2016 can be approximated by the models C=2549t+1.1t2andR=341+3.2t where P is the year, with t=10 corresponding to 2010. (a) Write a function P that represents the annual profit of the company. (b) Use a graphing utility to graph C,R, and P in the same viewing window.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning