Brand Z's annual sales are affected by the sales of related products X and Y as follows: Each $1 million increase in sales of Brand X causes a $2.5 million decline in sales of Brand Z, whereas each $1 million increase in sales of Brand Y results in an increase of $0.4 million in sales of Brand Z. Currently, Brands X, Y, and Z are each selling $6 million per year. Model the sales of Brand Z using a linear function. (Let z = annual sales of Z (in millions of dollars), x = annual sales of X (in millions of dollars), and y= annual sales of Y (in millions of dollars).) Z= Need Help? Read It Watch It

Brand Z's annual sales are affected by the sales of related products X and Y as follows: Each $1 million increase in sales of Brand X causes a $2.5 million decline in sales of Brand Z, whereas each $1 million increase in sales of Brand Y results in an increase of $0.4 million in sales of Brand Z. Currently, Brands X, Y, and Z are each selling $6 million per year. Model the sales of Brand Z using a linear function. (Let z = annual sales of Z (in millions of dollars), x = annual sales of X (in millions of dollars), and y= annual sales of Y (in millions of dollars).) Z= Need Help? Read It Watch It

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 6EQ: Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of...

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Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?
The number of patrol officers needed on staff depends on the crime rate of the county, which is calculated based on the number of crimes per year. At a 3% crime rate, the county hires 200 officers per 10,000 people in the population. For every 0.1% increase in crime rate, an additional 5 officers are hired per 10,000 people in the population. For every 0.1% below 3% crime rate, 3 fewer officers are hired. A 3% sign-on bonus is offered for officers with no experience when there is a 5% to 10% shortage in the number of officers employed. A 5% sign-on bonus is offered for officers with no experience when there is an 11% or higher shortage in the number of officers employed. A 6% sign-on bonus is offered for officers with at least 3 years of experience when there is a 5% to 10% shortage in the number of officers employed. A 10% sign-on bonus is offered for officers with at least 3 years of experience when there is an 11% or higher shortage in the number of officers employed. County…
Brand Z's annual sales are affected by the sales of related products X and Y as follows: Each $1 million increase in sales of brand X causes a $6.5 million decline in sales of brand Z, whereas each $2 million increase in sales of brand Y results in an increase of $29 million in sales of brand Z. Currently, brands X and Y are each selling $2 million per year, and brand Z is selling $61 million per year. Model the sales of brand Z using a linear function. (Let z = annual sales of Z (in millions of dollars), x = annual sales of X (in millions of dollars), and y = annual sales of Y (in millions of dollars).)
Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars (1,000s) Revenue ($ millions) Company A 11.5 116 Company B 10 137 Company C 9 102 Company D 5.5 39 Company E 4.2 38 Company F 3.3 30 (a) Develop a scatter diagram with the number of cars in service as the independent variable. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? (c) Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal…
Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 116 Company B 10.0 133 Company C 9.0 98 Company D 5.5 37 Company E 4.2 40 Company F 3.3 32 a.Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal places.) b. For every additional car placed in service, estimate how much annual revenue will change (in dollars). (Round your answer to the nearest integer.) Annual revenue will increase by $ , for every additional car placed in…
Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 118 Company B 10.0 137 Company C 9.0 102 Company D 5.5 39 Company E 4.2 40 Company F 3.3 32 (a) Develop a scatter diagram with the number of cars in service as the independent variable. A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on…
Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 118 Company B 10.0 133 Company C 9.0 98 Company D 5.5 37 Company E 4.2 40 Company F 3.3 30 (a) Develop a scatter diagram with the number of cars in service as the independent variable. A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on…
A man has $420,000 invested in three rental properties. One property earns 6.5% per year on the investment, the second earns 9%, and the third earns 8%. The total annual earnings from the three properties is $34,450, and the amount invested at 8% equals the sum of the first two investments. Let x equal the investment at 6.5%, y equal the investment at 9%, and z represent the investment at 8%. Complete parts (a) through (d) below. a. Write an equation that represents the sum of the three investments. nothing (Type an equation. Do not include the $ symbol in your answer.) b. Write an equation that states that the sum of the returns from all three investments is $34,450. nothing (Type an equation. Do not include the $ symbol in your answer.) c. Write an equation that states that the amount invested at 8% equals the sum of the other two investments. nothing (Type an equation. Do not include the $ symbol in your answer.) d. Solve the system of equations…
A man has $380,000 invested in three rental properties. One property earns 7,5% per year on the investment, the second earns 7%, and the third earns 9%. The total annual earnings from the three properties is $30,750, and the amount invested at 9% equals the sum of the first two investments. Let x equal the investment at 7.5%, y equal the investment at 7%, and z represent the investment at 9%. Complete parts (a) through (d) below. x+y+z=380000 (Type an equation. Do not include the $ symbol in your answer.) b. Write an equation that states that the sum of the returns from all three investments is $30,750. 0.075x+0.07y +0.09z = 30,750 (Type an equation. Do not include the $ symbol in your answer.) c. Write an equation that states that the amount invested at 9% equals the sum 'of the other two investments. > z =x+y (Type an equation. Do not include the $ symbol in your answer.) d. Solve the system of equations to find how much is invested in each property. O A. There is one solution. The…
. In 2010, of a total of 67,000 rooms on the Las Vegas Strip, Caesars Entertainment managed 22,880, while MGM Resorts managed over 12,000. However, owing to the Great Recession and new hotel openings, between 2008 and 2010, MGM's hotel occupancy decreased from 92% to 89%, while its average daily room rate fell from $148 to $108. Meanwhile, CityCenter, managed by MGM Resorts, and the Cosmopolitan opened with 4,000 and 3,000 rooms respectively, and the 1,720-room Sahara closed. (Sources: Caesars Entertainment Corp., Annual Report 2010; MGM Resorts, Annual Report 2010; "Sahara's closure on May 16 will mark `the end of an era'," Las Vegas Sun, March 11, 2011.) (a) Using a suitable figure, explain how the opening of CityCenter and the Cosmopolitan affects the residual demand for an existing hotel and how it should adjust prices. (b) If MGM Resorts had not reduced its room rates, what would have been the effect on occupancy? (c) Use the Cournot model to explain…
The demand for MICHTEC's products is related to the state of the economy. If the economy is expanding next year (an above-normal growth in GNP), the company expects sales to be $90 million. If there is a recession next year (a decline in GNP), sales are expected to be $75 million. If next year is normal (a moderate growth in GNP), sales are expected to be $85 million. MICHTEC's economists have estimated the chances that the economy will be either expanding, normal, or in a recession next year at 0.3, 0.5, and 0.2, respectively. The expected annual sales is million. The standard deviation of annual sales is The coefficient of variation of annual sales is million.