Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 6.3, Problem 12E
To determine
(a)
To plot:
The graph of the profit as a function of the number of widgets manufactured in a week.
To determine
(b)
The marginal profit if the firm produces
To determine
(c)
The marginal profit if the firm produces
To determine
(d)
To find:
Number of widgets to be produced in a week to maximize profit.
To determine
(e)
The marginal profit at the production level found in part (d).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Ch. 6.1 - ReminderRound all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...Ch. 6.1 - Reminder Round all answers to two decimal places...
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Velocity What is the rate of change in directed...Ch. 6.1 - Sign of VelocityWhen directed distance is...Ch. 6.1 - Sign of VelocityWhen the graph of directed...Ch. 6.1 - Constant VelocityWhen velocity is constant, what...Ch. 6.1 - Constant Velocity When the graph of directed...Ch. 6.1 - Prob. 6SBECh. 6.1 - Prob. 7SBECh. 6.1 - Prob. 8SBECh. 6.1 - Prob. 9SBECh. 6.1 - Prob. 10SBECh. 6.1 - Change in Direction A graph of directed distance...Ch. 6.1 - Prob. 12SBECh. 6.2 - Prob. 1ECh. 6.2 - Reminder Round all answers to two decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Prob. 8ECh. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - ReminderRound all answers to two decimal places...Ch. 6.2 - Reminder Round all answers to two decimal places...Ch. 6.2 - ReminderRound all answers to two decimal places...Ch. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - SKILL BUILDING EXERCISES Marginal Cost: Let C(n)...Ch. 6.2 - SKILL BUILDING EXERCISES Marginal Profit: Your...Ch. 6.2 - SKILL BUILDING EXERCISES Buying for the Short...Ch. 6.2 - SKILL BUILDING EXERCISES Buying a company: You are...Ch. 6.2 - Meaning Of Rate Change: What is the common term...Ch. 6.2 - A Mathematical Term: If f=f(x), then we use dfdx...Ch. 6.2 - Sign of the Derivative: Suppose f=f(x). What is...Ch. 6.2 - Prob. 8SBECh. 6.2 - Prob. 9SBECh. 6.2 - Prob. 10SBECh. 6.2 - Prob. 11SBECh. 6.2 - Prob. 12SBECh. 6.2 - Prob. 13SBECh. 6.2 - Prob. 14SBECh. 6.2 - Prob. 15SBECh. 6.2 - Prob. 16SBECh. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Reminder Round all answers to two decimal places...Ch. 6.3 - Reminder Round all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Prob. 12ECh. 6.3 - Rate of Change for a Linear Function If f is the...Ch. 6.3 - Rate of Change for a Linear Function If f is the...Ch. 6.3 - Rate of Change from Data Suppose f=f(x) satisfies...Ch. 6.3 - Rate of Change from Data Suppose f=f(x) satisfies...Ch. 6.3 - Prob. 5SBECh. 6.3 - Prob. 6SBECh. 6.3 - Estimating Rates of Change By direct calculation,...Ch. 6.3 - Estimating Rates of Change with the CalculatorMake...Ch. 6.3 - Prob. 9SBECh. 6.3 - Prob. 10SBECh. 6.3 - Prob. 11SBECh. 6.3 - Prob. 12SBECh. 6.3 - Prob. 13SBECh. 6.3 - Prob. 14SBECh. 6.4 - ReminderRound all answers to two decimal places...Ch. 6.4 - Reminder Round all answers to two decimal places...Ch. 6.4 - Reminder Round all answers to two decimal places...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 1SBECh. 6.4 - Prob. 2SBECh. 6.4 - Prob. 3SBECh. 6.4 - New Equation of Change? The tax liability T in...Ch. 6.4 - Prob. 5SBECh. 6.4 - Prob. 6SBECh. 6.4 - Prob. 7SBECh. 6.4 - Prob. 8SBECh. 6.4 - Prob. 9SBECh. 6.4 - Prob. 10SBECh. 6.4 - A Leaky BalloonA balloon leaks air changes volume...Ch. 6.4 - Prob. 12SBECh. 6.4 - Solving an Equation of Change Solve the equation...Ch. 6.4 - Prob. 14SBECh. 6.4 - Filling a Tank The water level in a tank rises...Ch. 6.4 - Solving an Equation of Change Solve the equation...Ch. 6.5 - Reminder Round all answers to two decimal places...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 1SBECh. 6.5 - Prob. 2SBECh. 6.5 - Prob. 3SBECh. 6.5 - Prob. 4SBECh. 6.5 - Prob. 5SBECh. 6.5 - Prob. 6SBECh. 6.5 - WaterWater flows into a tank, and a certain part...Ch. 6.5 - Prob. 8SBECh. 6.5 - Prob. 9SBECh. 6.5 - Prob. 10SBECh. 6.5 - Prob. 11SBECh. 6.5 - Prob. 12SBECh. 6.5 - Equation of ChangeFor the equation of change...Ch. 6.5 - Prob. 14SBECh. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Prob. 4CRCh. 6.CR - Prob. 5CRCh. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - Prob. 18CRCh. 6.CR - Reminder Round all answers to two decimal places...Ch. 6.CR - Prob. 20CR
Knowledge Booster
Similar questions
- ReminderRound all answers to two decimal places unless otherwise indicated. Minimum WageOn July 24, 2008, the federal minimum wage was 6.55perhour. On July 24, 2009, this wage was raised to 7.25perhour. If W(t) denotes the minimum wage, in dollars per hour, as function of time, in years, use the given information to estimate dWdt in 2009.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Household DebtThe graph in Figure 1.27 shows the average American household debt h as a function of the date d. Here h(d) represents house hold debt as a percentage of disposable income. a.Explain the meaning of h(1975) in practical terms, and use the graph to find its value. b.The graph reaches a maximum value. Estimate the maximum value and the year in which it occurred. FIGURE 1.27arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. River FlowThe graph in Figure 1.37 shows the mean flow F for the Arkansas River, in cubic feet of water per second, as a function of the time t, in months, since the start of the year. The flow is measured near the rivers headwaters in the Rocky Mountains. a.Use functional notation to express the flow at the end of July, and then estimate that value. b.When is the flow at its greatest? c.At what time is the flow increasing the fastest? FIGURE 1.37 Flow for the Arkansas River d.Estimate the average rate of change per month in the flow during the first 2 months of the year. e.In light of the source of the Arkansas River, interpret your answers to parts b, c, and d.arrow_forward
- Reminder: Round all answer to two decimal places unless otherwise indicated. 15.Total Cost The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To deter mine a formula for the total cost, we need to know the manufacturers fixed costs covering things such as plant maintenance and insurance, as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of 9000 per month and that the variable cost is 15 per widget so it costs 15 to produce 1 widget. a. Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. Be sure to state the units you use. b. Express using functional notation the total cost if there are 250 widgets produced in a month, and then calculate that value.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. InflationDuring a period of high inflation, a political leader was up for re-election. Inflation had been increasing during his administration, but he announced that the rate of increase of inflation was decreasing. Draw a graph of inflation versus time that illustrates this situation. Would this announcement convince you that economic conditions were improving?arrow_forwardReminder Round all answers to decimal places unless otherwise indicated. Health Plan The managers of an employee health plan for a firm have studied the balance B, in millions of dollars, in the plan account as a function of t, the number of years since the plan was instituted. They have determined that the rate of change dBdt in the account balance is given by the formula dBdt=10e0.1t12. a. Use your calculator to make a graph of dBdt versus t over the first 5 years of the plan. b. During what period is the account balance B decreasing? c. At what time is the account balance B at its minimum?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Sales Income The following table shows the net monthly income N for a real estate agency as a function of the monthly real estate sales s, both measured in dollars. s=Sales N=Netincome 450,000 4000 500,000 5500 550,000 7000 600,000 8500 a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in N. What pattern do you see? b. Use the average rate of change to estimate the net monthly income for monthly real estate sales of 520,000. In light of your answer to part a, how confident are you that your estimate is an accurate representation of the actual income? c. Would you expect N to have a limiting value? Be sure to explain your reasoning.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Sales Growth A study of the sales s, in thousands of dollars, of a product as a function of time t, in years, yields the equation of change dsdt=0.3s(4s). This is valid for s less than 5. a.What level of sales will be attained in the long run? b.What is the largest rate of growth in sales?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. The height of the winning pole vault in the early years of the modern Olympic Games can be modeled as a function of time by the formula H=0.05t+3.3 Here t is the number of years since 1900, and H is the winning height in meters. One meter is 39.37 inches. a. Calculate H(4) and explain in practical terms what your answer means. b. By how much did the height of the winning pole vault increase from 1900 to 1904? From 1904 to 1908?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Travel Time The time T, in hours, required to drive 100miles is a function of the average speed s, in miles per hour. The formula is T=100s. a. Make a graph T versus s covering speeds up to 70milesperhour. b. Calculate T(25) and explain in practical terms what your answer means. c. Explain in practical terms the behavior of the graph near the pole at s=0.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Total Revenue and Profit This is a continuation of Exercise 13. The total revenue R for a manufacturer during a given time period is a function of the number N of items produced during that period. In this exercise, we assume that the selling price per unit of the item is a constant, so it does not depend on the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. If the profit is zero, then the manufacturer is at a break-even point. We consider again the manufacturer of widgets in Exercise 13 with fixed costs of 1500 pr month and a variable cost of 20 per widget. Suppose the manufacturer sells 100 widgets for 2300 total. a. Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as function of the number N of widgets produced in a month. b. Use a formula to express the monthly profit P, in dollars, of this manufacturer as function of the number of widgets produced in a month. Explain how the slope and initial of P are derived from the fixed costs, variable cost, and price per widget. c. What is the break-even point for this manufacturer? d. Make graphs of total monthly cost and total monthly revenue. Include monthly production levels up to 1200 widgets. What is the significance of the point where the graphs cross?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Total Cost The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know two things. The first is the manufacturers fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the Variable cost. Suppose that a manufacturer of widgets has fixed costs of 1500 per month and that the variable cost is 20 per widget so it costs 20 to produce 1 widget. a. Explain why the function giving the total monthly cost C, in dollars, of this widget manufacturer in terms of the number N of widgets produced in a month is linear. Identify the slope and initial value of this function, and write down a formula. b. Another widget manufacturer has a variable cost of 12 per widget, and the total is 3100 when 150 widgets are produced in a month. What are the fixed costs for this manufacturer? c. Yet another widget manufacturer has determined the following: The total cost is 2700 when 100 widgets are produced in a month, and the total cost is 3500 when 150 widgets are produced in a month. What are the fixed costs and variable costs for this manufacturer?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning