Concept explainers
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 manufacturer’s 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.
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Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra: Graphs and Models (6th Edition)
A Graphical Approach to College Algebra (6th Edition)
Glencoe Algebra 2 Student Edition C2014
Elementary Algebra: Concepts and Applications (10th Edition)
College Algebra (7th Edition)
Elementary Algebra For College Students (9th Edition)
- EXERCISES Reminder Round all answers to two decimal places unless otherwise indicated. Fixed and Variable Costs The fixed cost for a manufacturing company are the costs, such as rent or repayment of a startup loan, that the company must pay each month no matter how many items are produced. The variable cast is the cost of producing a single item. Assume that when a company produces I items per month, the total monthly cost is C=30I+1400 dollars. Identify the fixed costs and the variable cost in this equation.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_forwardReminderRound all answers to two decimal places unless otherwise indicated. Equilibrium PriceThis is a continuation of Exorcise 5. The equilibrium price is the price where the supply and demand are the same. In Figure 1.31, the supply curve is in red and the demand curve is in blue. Use this graph to estimate the equilibrium price. How many items are supplied at the equilibrium price? FIGURE 1.31 5. Supply and Demand CurvesA supply curve is a graph that shows the quantity of a product that is made available by suppliers as a function of the price. Similarly, a demand curve is a graph that shows the quantity of a product that consumers are willing to purchase as a function of the price. Examples of supply and demand curves are shown in Figures 1.29 and 1.30. a.Explain in practical terms what the supply curve in Figure 1.29 tells us. b.Explain in practical terms what the demand curve in Figure 1.30 tells us. FIGURE 1.29 A Supply curve FIGURE 1.30 A demand curvearrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Real Estate Sales A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities, and supplies. It earns its money by taking a percentage commission on total real estate sales. During the month of July, the agency had total sales of 832,000 and showed a net income after paying fixed costs of 15,704. In August, total sales were 326,000 with a net income of only 532. a. Use a formula to express net income as a linear function of total sales. Be sure to identify what the letters that you use mean. b. Plot the graph of net income and identify the slope and vertical intercept. c. What are the real estate agencys fixed monthly costs? d. What percentage commission does the agency take on the sale of a home? e. Find the horizontal intercept and explain what this number means to the real estate agency.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Profit 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. In this exercise, we measure all monetary values in dollars. To determine a formula for the total cost, we need to know the manufacturers fixed costs covering such things 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. The total revenue R for a manufacturer during a given time period is also a function of the number N of items produced during that period. To determine a formula for the total monthly revenue, we need to know the selling price p per unit of the item, which in general is also a function of N. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. Suppose that a manufacturer of widgets has a fixed costs of 2000 per month and that the variable cost is 30 per widget. Further, the manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. Number N Price p 200 41.00 250 40.50 300 40.00 350 39.50 a.Use a formula to express the total monthly cost C of this manufacturer as a function of N. b.Use the table to find a linear model of p as a function of N. c.Use your answer to part b to find a formula expressing the total monthly revenue R as function of N. d.Use your answers to part a and part c to find a formula expressing the monthly profit P as a function of N. What type of function is the profit: linear or quadratic? e.Find the two monthly production levels at which the manufacturer just breaks even that is, where the profit is zero.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. World Copper Production World production of copper, in millions of tons per year, from 1900 to 2000 is given by C=0.51.033t, where t is the time in years since 1900. a.What production level does this model give for the year 2000? b.If this model were extended to 2025, how could you use your knowledge of copper production in 2024 to estimate copper production in 2025?arrow_forward
- Getting a Formula In Exercises S-4 through S-13, a verbal description of a function is given. Use a formula to express the function. You sell lemonade for 25 cents per glass. You invested 2.00 in the ingredients. Write a formula that gives the profit P=P(n) as a function of the number n of glasses you sell.arrow_forwardReminderRound 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_forwardGetting a Formula In Exercises S-4 through S-13, a verbal description of a function is given. Use a formula to express the function. You pay 500 to rent a special area in a restaurant. In addition, you pay 10 for each guest. Write a formula that gives your total cost C, in dollars, as a function of the number n of dinner guests.arrow_forward
- ReminderRound 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_forwardReminder: Round all answer to two decimal places unless otherwise indicated. a. How much does it cost to prepare and mail a 3-page letter if your secretary spends 2 hours on typing and corrections? b. Use a formula to express the cost of preparing and mailing a letter as a function of the number of pages in the letter and the time it takes your secretary to type it. Identify the function and each of the variables you use, and state the units. c. Use the function you made in part b to find the cost of preparing and mailing a 2-page letter that it takes your secretary 25 minutes to type. Note: 25 minutes is 25/60 hour.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Magazine SalesThe following table shows the income from sales of a certain magazine, measured in thousands of dollars, at the start of the given year. Year Income 2009 7.76 2010 8.82 2011 9.88 2012 10.94 2013 12.00 2014 13.08 2015 14.26 2016 15.54 Over an initial period the sales grew at a constant rate, and over the rest of the time the sales grew at a constant percentage rate. Calculate differences and ratios to determine what these time periods are, and find the growth rate or percentage growth rate, as appropriate.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning