Concept explainers
Business The annual cost
where
(a) Write a function
(b) Use a graphing utility to graph
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Chapter 2 Solutions
College Algebra
- Profit The yearly profit P for a widget producer is a function of the number n of widgets sold. The formula is P=180+100n4n2. Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to level of 20 thousand widgets sold. a. Make a graph of P versus n. b. Calculate P0 and explain in practical terms. What your answer means. c. What profit will the producer make if 15 thousand widgets are sold?. d. The break-even point is the sales level at which the profit is 0. Approximate the break-even point for this widget producer. e. What is the largest profit possible?arrow_forwardMaximum Revenue A small theater has a seating capacity of 2000.When the ticket price is 20,attendance is 1500.For each 1decrease in price, attendance increases by 100. (a) Write the revenue R of the theater as a function of ticket price x. (b) What ticket price will yield a maximum revenue? What is the maximum revenue?arrow_forwardProfit A company that produces calculators estimates that the profit P(in dollars) from selling a specific model of calculator is given by P=152x3+7545x2169,625,0x45 where xis the advertising expense (in tens of thousands of dollars).For this model of calculator, an advertising expense of $400,000(x=40)results in a profit of $2,174,375. (a) Use a graphing utility to graph the profit function. (b) Use the graph from part (a) to estimate another amount the company can spend on advertising that results in the same profit. (c) Use synthetic division to confirm the result of part (b) algebraically.arrow_forward
- Recycling 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_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+1.1t2 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_forwardProfit The demand equation for a microwave oven is given by p=1400.0001x, where p is the unit price (in dollars) of the microwave oven and x is the number of units sold. The cost equation for the microwave oven is C=80x+150,000, where C is the total cost (in dollars) and x is the number of units produced. The total profit P obtained by producing and selling x units is modeled by P=xpC. (a) Find the profit function P in terms of x. (b) Find the profit when 250,000 units are sold. (c) Find the unit price when 250,000 units are sold. (d) Find (if possible) the unit price that will yield a profit of 10 million dollars. If not possible, explain why.arrow_forward
- Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0r70 Where y represents the life expectancy and t is the time in years, with t=0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. (d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explainarrow_forwardSeizure of Illegal Drugs The cost C(in millions of dollars) for the federal government to seize p%of an illegal drug as it enters the country is given by C=528p100p,0p100. (a) Use a graphing utility to graph the cost function. (b) Find the costs of seizing 25%,50%,and 75%of the drug. (c) According to the model, is it possible to seize 100%of the drug? Explain.arrow_forwardProfit 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_forward
- Ecology The cost C (in millions of dollars) of removing p of the industrial and municipal pollutants discharged into a river is given by C=225p100p,0p100. (a) Use a graphing utility to graph the cost function. (b) Find the costs of removing 10,40,and75 of the pollutants. (c) According to the model, is it possible to remove 100 of the pollutants? Explain.arrow_forwardPopulation Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0t70 Where y represents the life expectancy and t is the time in years, with t = 0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. verify your answer algebraically. (d) Find the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now?arrow_forwardProfit The profit P, in thousands of dollars that a manufacturer makes is a function of the number N of items produced in a year, and the formula is P=0.2N2+3.6N9. a. Express using functional notation the profit at a production level of 5 items per year, and then calculate that value. b. Determine the two break-even points for this manufacturesthat is, the two production levels at which the profit is zero. c. Determine the maximum profit if the manufacturer can produce at most 20 items in a year.arrow_forward
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