Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Textbook Question
Chapter 2.3, Problem 21E
BREAK-EVEN POINTS AND MAXIMIZATION
Assume that costs and expenses for Continental
Divide Mining can be modeled by
where t is the number of years past 2003.
(a) Use R(t) as given in Problem 20 and form the profit function (as a function of time).
(b) Use the function from (a) to find the year in which maximum profit occurs.
(c) Graph the profit function from (a) and the data points from the table.
(d) Through the decade from 2011 to 2021, does the function project increasing or decreasing profits? Do the data support this trend (as far as it goes)?
(e) How might management respond to this kind of projection?
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Chapter 2 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 2.1 - The factoring method for solving a quadratic...Ch. 2.1 - Solve the following equations by factoring.
Ch. 2.1 - Prob. 3CPCh. 2.1 - Prob. 4CPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 6E
Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 8ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 10ECh. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 12ECh. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - Prob. 16ECh. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 36ECh. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - In Problems 43-46, multiply both sides of the...Ch. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Applications Profit If the profit from the sale of...Ch. 2.1 - Profit If the profit from the sale of x units of a...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Flight of a ball If a ball is thrown upward at 96...Ch. 2.1 - Flight of a ball A tennis ball is thrown into the...Ch. 2.1 - Wind and pollution The amount of airborne...Ch. 2.1 - Drug sensitivity The sensitivity S to a drug is...Ch. 2.1 - 57. Corvette acceleration The time t, in seconds ,...Ch. 2.1 - 59. Marijuana use For the years since 2001 , the...Ch. 2.1 - Prob. 56ECh. 2.1 - 61. Percent profit Ace Jewelry Store sold a...Ch. 2.1 - Tourism spending The global spending on travel and...Ch. 2.1 - Prob. 59ECh. 2.1 - 64. Velocity of blood Because of friction from the...Ch. 2.1 - 65. Body-heat loss The model for body-heat loss...Ch. 2.1 - 66. Depth of Fissure A fissure in the earth...Ch. 2.2 - Name the graph of a quadratic function.
Ch. 2.2 - (a) What is the coordinate of the vertex of ?
(b)...Ch. 2.2 - Prob. 3CPCh. 2.2 - Prob. 4CPCh. 2.2 - Prob. 5CPCh. 2.2 - In Problems 1-6,(a)find the vertex of the graph of...Ch. 2.2 - Prob. 2ECh. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problem 1-6,(a)find the vertex of the graph of...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 7-12,determine whether each...Ch. 2.2 - In Problems7-12,determine whether each functions...Ch. 2.2 - In Problems 7-12,determine whether each function’s...Ch. 2.2 - In Problem 7-12, determine whether each function’s...Ch. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - In Problems , graph each function with a graphing...Ch. 2.2 - Prob. 21ECh. 2.2 - In Problem 21 and 22, find the average rate of...Ch. 2.2 - In Problems , find the vertex and zeros and use...Ch. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Profit The daily profit from the sale of a product...Ch. 2.2 - Profit The daily profit from the sale of x units...Ch. 2.2 - 33. Crop Yield The yield in bushels from a grove...Ch. 2.2 - 34. Stimulus-response One of the early results in...Ch. 2.2 - Drug Sensitivity The sensitivity S to a drug is...Ch. 2.2 - 36. Maximizing an enclosed area Iffeet of fence
...Ch. 2.2 - Photosynthesis The rate of photosynthesis R for a...Ch. 2.2 - 38. Projectiles A ball thrown vertically into the...Ch. 2.2 - Projectiles Two projectiles are shot into the air...Ch. 2.2 - Flow rates of water The speed at which water...Ch. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Apartment rental The owner of an apartment...Ch. 2.2 - Revenue The owner of a skating rink rents the...Ch. 2.2 - Pension resources The Pension Benefit Guaranty...Ch. 2.2 - Prob. 46ECh. 2.2 - Health care costs per capita Rising health care...Ch. 2.2 - Women in the workforce Using U.S. Census Bureau...Ch. 2.2 - Prob. 49ECh. 2.2 - E-commerce Online sales in the United States are...Ch. 2.3 - The point of intersection of the revenue function...Ch. 2.3 - If and , finding the break-even points requires...Ch. 2.3 - Prob. 3CPCh. 2.3 - Prob. 4CPCh. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION
1.The total...Ch. 2.3 - 2. If a firm has the following cost and revenue...Ch. 2.3 - 3.If a company has total costs
And total revenues...Ch. 2.3 - 4. If total costs are and total revenues
Are ,find...Ch. 2.3 - Given that profit is P(x)=11.5x-0.1x2-150 And that...Ch. 2.3 - 6.If the profit function for a firm is given by...Ch. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION Find the...Ch. 2.3 - 8.Find the maximum revenue for the revenue...Ch. 2.3 - 9.If in a monopoly market the demand for a...Ch. 2.3 - 10.If in a monopoly market the demand for a...Ch. 2.3 - The profit function for a certain commodity is...Ch. 2.3 - The profit function for a firm making widgets is ...Ch. 2.3 - (a) Graph the profit function .
(b) Find the...Ch. 2.3 - Prob. 14ECh. 2.3 - (a) Form the profit function for the cost and...Ch. 2.3 - Prob. 16ECh. 2.3 - 17. Suppose a company has fixed costs of and...Ch. 2.3 - 18. Suppose a company has fixed costs of and...Ch. 2.3 - Prob. 19ECh. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION Assume that...Ch. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION Assume that...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - 25. If the supply function for a commodity is and...Ch. 2.3 - If the supply function for a commodity is and the...Ch. 2.3 - If the demand function for a commodity is given by...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a certain...Ch. 2.3 - The supply function for a product is , while the...Ch. 2.3 - The supply and demand for a product are given by ...Ch. 2.3 - For the product in problem 31, if a $22 tax is...Ch. 2.3 - Prob. 34ECh. 2.4 - All constant functions [such as ] have graphs that...Ch. 2.4 - Which of the following are polynomial...Ch. 2.4 - A third-degree polynomial can have at most _____...Ch. 2.4 - Prob. 4CPCh. 2.4 - Prob. 5CPCh. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problem 13, decide whether each function whose...Ch. 2.4 - In problem 14, decide whether each function whose...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 -
Ch. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - In Problems 23-28, graph the function.
28.
Ch. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - 34. If
find the following.
(b) (c) (d)...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - [Type here]
In Problems 35-40, (a) graph each...Ch. 2.4 - [Type here]
In Problems 35-40, (a) graph each...Ch. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - 41. Postal restrictions If a box with a square...Ch. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - 45. Pollution Suppose that the cost (in dollars)...Ch. 2.4 - Average cost If the weekly total cost of producing...Ch. 2.4 - Area If 100 feet of fence is to be used to enclose...Ch. 2.4 - Water usage The monthly charge for water in a...Ch. 2.4 - Prob. 49ECh. 2.4 - Commercial electrical usage The monthly charge (in...Ch. 2.4 - First-class postage The postage charged for...Ch. 2.4 - Income tax In a given year the U.S. federal income...Ch. 2.4 - Prob. 53ECh. 2.4 - Prob. 55ECh. 2.5 - The following table gives the Social Security...Ch. 2.5 - Prob. 2CPCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 5ECh. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 15ECh. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - emission The following table gives the millions...Ch. 2.5 - Disposable income Disposable income is the amount...Ch. 2.5 - Diabetes As the following table shows ,...Ch. 2.5 - Wind chill The table gives the wind chill...Ch. 2.5 - Developing economies The developing economies’...Ch. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - National health care The table shows the national...Ch. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - For each function in Problems 19-24, find the...Ch. 2 - For each function in Problems 19-24, find the...Ch. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - [Type here]
In Problems 25-30, use a graphing...Ch. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - In Problems 25-30, use a graphing calculator to...Ch. 2 - The supply function for a product is 2pq10=0,...Ch. 2 - The supply and demand for a product are given by...Ch. 2 - 33.For the product in Problem 31,if a $22 tax is...Ch. 2 - Prob. 34RECh. 2 - In Problems 33-36, a graph is given. Use the graph...Ch. 2 - Prob. 36RECh. 2 - 37. Sketch a graph of each of the following basic...Ch. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - In Problems 40 and 41 ,graph each function.
40. ...Ch. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - 49.Profit The profit for a product is given by...Ch. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - 54. Market equilibrium
(a) Suppose the supply...Ch. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Break-even points If total costs for a product are...Ch. 2 - Break-even points If total costs for a commodity...Ch. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Maximum profit Given and , find the level of...Ch. 2 - Break-even and profit maximization A certain...Ch. 2 - 63. Diabetes The rise of adult diabetes in the...Ch. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - 68. Average annual wage The tables below give...Ch. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Which of the following three graphs is the graph...Ch. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Suppose the supply and demand functions for a...Ch. 2 - Suppose a company’s total cost a product is given...Ch. 2 - Prob. 19TCh. 2 - Prob. 20TCh. 2 - Prob. 1EAGP1Ch. 2 - Prob. 2EAGP1Ch. 2 - Prob. 3EAGP1Ch. 2 - Prob. 4EAGP1Ch. 2 - Prob. 5EAGP1Ch. 2 - Prob. 6EAGP1Ch. 2 - Prob. 7EAGP1Ch. 2 - Prob. 1EAGP2Ch. 2 - Prob. 2EAGP2Ch. 2 - Prob. 3EAGP2Ch. 2 - Prob. 4EAGP2Ch. 2 - Prob. 5EAGP2Ch. 2 - Prob. 6EAGP2Ch. 2 - Prob. 7EAGP2Ch. 2 - Prob. 8EAGP2
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