Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 5.I, Problem 7RE
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To calculate: The value of unknown from the equation
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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model.
Interpret the…
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
To
Hamilton Butler
Clermont
Southern Gas
10
20
15
Northwest Gas
12
15
18
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
Assignment 3 graph.docx
Score: 1 out of 1
Comment:
(b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs (in thousands of…
Chapter 5 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 5.I - Solve the following equations for the unknown and...Ch. 5.I - Prob. 2TIECh. 5.I - Prob. 3TIECh. 5.I - Prob. 4TIECh. 5.I - Solve the following equations for the unknown and...Ch. 5.I - Prob. 6TIECh. 5.I - Prob. 7TIECh. 5.I - Prob. 8TIECh. 5.I - Prob. 9TIECh. 5.I - For the following statements, underline the key...
Ch. 5.I - Prob. 1RECh. 5.I - Prob. 2RECh. 5.I - Prob. 3RECh. 5.I - Prob. 4RECh. 5.I - Prob. 5RECh. 5.I - Prob. 6RECh. 5.I - Prob. 7RECh. 5.I - Prob. 8RECh. 5.I - Prob. 9RECh. 5.I - Prob. 10RECh. 5.I - Prob. 11RECh. 5.I - Prob. 12RECh. 5.I - Prob. 13RECh. 5.I - Prob. 14RECh. 5.I - Prob. 15RECh. 5.I - Prob. 16RECh. 5.I - Prob. 17RECh. 5.I - For the following statements, underline the key...Ch. 5.I - Prob. 19RECh. 5.I - Prob. 20RECh. 5.I - Prob. 21RECh. 5.I - Prob. 22RECh. 5.I - Prob. 23RECh. 5.I - Prob. 24RECh. 5.I - For the following statements, underline the key...Ch. 5.I - Prob. 26RECh. 5.I - Prob. 27RECh. 5.I - Prob. 28RECh. 5.I - Prob. 29RECh. 5.I - Prob. 30RECh. 5.I - For the following statements, underline the key...Ch. 5.I - Grouping symbols are used to arrange numbers,...Ch. 5.II - Don and Chuck are salespeople for Security One...Ch. 5.II - One-third of the checking accounts at the...Ch. 5.II - Prob. 13TIECh. 5.II - Prob. 14TIECh. 5.II - Last week Comfy Cozy Furniture sold 520 items. It...Ch. 5.II - REI (Recreational Equipment Incorporated) sells a...Ch. 5.II - Prob. 17TIECh. 5.II - Prob. 1RECh. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Prob. 4RECh. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Prob. 16RECh. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Set up and solve equations for the following...Ch. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Prob. 22RECh. 5.II - Prob. 23RECh. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Prob. 25RECh. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - Use ratio and proportion to solve the following...Ch. 5.II - 30. In a move to provide additional sales for U.S....Ch. 5 - A(n) ______ is a mathematical statement describing...Ch. 5 - A mathematical statement expressing a relationship...Ch. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - The numerical value of the unknown that makes an...Ch. 5 - Prob. 6CRCh. 5 - 7. To transpose means to bring a term from one...Ch. 5 - Prob. 8CRCh. 5 - 9. To prove the solution of an equation, we...Ch. 5 - Prob. 10CRCh. 5 - Prob. 11CRCh. 5 - 12. A comparison of two quantities by division is...Ch. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 1ATCh. 5 - Prob. 2ATCh. 5 - Solve the following equations for the unknown and...Ch. 5 - Prob. 4ATCh. 5 - Prob. 5ATCh. 5 - Prob. 6ATCh. 5 - Prob. 7ATCh. 5 - Prob. 8ATCh. 5 - Prob. 9ATCh. 5 - Prob. 10ATCh. 5 - For the following statements, underline the key...Ch. 5 - Prob. 12ATCh. 5 - Prob. 13ATCh. 5 - Prob. 14ATCh. 5 - Prob. 15ATCh. 5 - For the following statements, underline the key...Ch. 5 - Prob. 17ATCh. 5 - Prob. 18ATCh. 5 - Set up and solve equations for each of the...Ch. 5 - Set up and solve equations for each of the...Ch. 5 - Prob. 21ATCh. 5 - Set up and solve equations for each of the...Ch. 5 - Prob. 23ATCh. 5 - Set up and solve equations for the following...Ch. 5 - Set up and solve equations for the following...Ch. 5 - Set up and solve equations for the following...Ch. 5 - Set up and solve equations for the following...Ch. 5 - Set up and solve equations for the following...Ch. 5 - Set up and solve equations for the following...Ch. 5 - Prob. 30ATCh. 5 - Use ratio and proportion to solve the following...Ch. 5 - Use ratio and proportion to solve the following...Ch. 5 - Use ratio and proportion to solve the following...Ch. 5 - 34. One special type of ratio is known as a rate....
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- Use the method of undetermined coefficients to solve the given nonhomogeneous system. dx dt = 2x + 3y − 8 dy dt = −x − 2y + 6 X(t) =arrow_forwardAs discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let ds ≥ R − Rs with ds ≥ 0. Then make the objective function: Min 1 5 5 s = 1 ds2. Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund…arrow_forwardCalculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forward
- For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forward
- The Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forward
- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward
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