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11:17 AM Wed Apr 1 * 41%O Business ana Econ omics 67. Optimizing revenue. A hotel owner notices that she rents y rooms per night when the price is x dollars per room, with y = 200 – 2x. a. Find R(x), the total revenue generated per night when the price of each room is x dollars. b. Find the relative extremum of R, and interpret this result. 68. Optimizing revenue. A software developer notices that the number y of downloads of an app (in thousands) is related to the price x (in dollars) of the app by y = 2.6 – 0.4x . a. Find R(x), the total revenue generated when the price of the app is x dollars. b. Find the relative extremum of R, and interpret this result. 69. Optimizing revenue. An artist sells y sculptures when the price of each sculpture is x dollars, where y = 500 - 5х. a. Find R(x), the total revenue generated when the price of each sculpture is x dollars. b. Find the relative extremum of R, and interpret this result. 70. Optimizing yield. Each apple tree yields y apples when there are x trees in an orchard, where y = 300 – 6x . a. Find R(x), the total yield generated when there are x apple trees in the orchard. b. Find the relative extremum of R, and interpret this result. Life and Physical Sciences 71. Solar eclipse. On July 2, 2019, a total solar eclipse was observable over the South Pacific Ocean and parts of South America. (Source: eclipse.gsfc.nasa.gov.) The path of the eclipse is modeled by f(t) = 0.00259t² – 0.457t + 36.237, where f(t) is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse was visible? 278

11:17 AM Wed Apr 1 * 41%O Business ana Econ omics 67. Optimizing revenue. A hotel owner notices that she rents y rooms per night when the price is x dollars per room, with y = 200 – 2x. a. Find R(x), the total revenue generated per night when the price of each room is x dollars. b. Find the relative extremum of R, and interpret this result. 68. Optimizing revenue. A software developer notices that the number y of downloads of an app (in thousands) is related to the price x (in dollars) of the app by y = 2.6 – 0.4x . a. Find R(x), the total revenue generated when the price of the app is x dollars. b. Find the relative extremum of R, and interpret this result. 69. Optimizing revenue. An artist sells y sculptures when the price of each sculpture is x dollars, where y = 500 - 5х. a. Find R(x), the total revenue generated when the price of each sculpture is x dollars. b. Find the relative extremum of R, and interpret this result. 70. Optimizing yield. Each apple tree yields y apples when there are x trees in an orchard, where y = 300 – 6x . a. Find R(x), the total yield generated when there are x apple trees in the orchard. b. Find the relative extremum of R, and interpret this result. Life and Physical Sciences 71. Solar eclipse. On July 2, 2019, a total solar eclipse was observable over the South Pacific Ocean and parts of South America. (Source: eclipse.gsfc.nasa.gov.) The path of the eclipse is modeled by f(t) = 0.00259t² – 0.457t + 36.237, where f(t) is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse was visible? 278

Principles of Economics 2e
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter16: Information, Risk, And Insurance
Section: Chapter Questions
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11:17 AM Wed Apr 1 * 41%O Business ana Econ omics 67. Optimizing revenue. A hotel owner notices that she rents y rooms per night when the price is x dollars per room, with y = 200 – 2x. a. Find R(x), the total revenue generated per night when the price of each room is x dollars. b. Find the relative extremum of R, and interpret this result. 68. Optimizing revenue. A software developer notices that the number y of downloads of an app (in thousands) is related to the price x (in dollars) of the app by y = 2.6 – 0.4x . a. Find R(x), the total revenue generated when the price of the app is x dollars. b. Find the relative extremum of R, and interpret this result. 69. Optimizing revenue. An artist sells y sculptures when the price of each sculpture is x dollars, where y = 500 - 5х. a. Find R(x), the total revenue generated when the price of each sculpture is x dollars. b. Find the relative extremum of R, and interpret this result. 70. Optimizing yield. Each apple tree yields y apples when there are x trees in an orchard, where y = 300 – 6x . a. Find R(x), the total yield generated when there are x apple trees in the orchard. b. Find the relative extremum of R, and interpret this result. Life and Physical Sciences 71. Solar eclipse. On July 2, 2019, a total solar eclipse was observable over the South Pacific Ocean and parts of South America. (Source: eclipse.gsfc.nasa.gov.) The path of the eclipse is modeled by f(t) = 0.00259t² – 0.457t + 36.237, where f(t) is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse was visible? 278
Transcribed Image Text:11:17 AM Wed Apr 1 * 41%O Business ana Econ omics 67. Optimizing revenue. A hotel owner notices that she rents y rooms per night when the price is x dollars per room, with y = 200 – 2x. a. Find R(x), the total revenue generated per night when the price of each room is x dollars. b. Find the relative extremum of R, and interpret this result. 68. Optimizing revenue. A software developer notices that the number y of downloads of an app (in thousands) is related to the price x (in dollars) of the app by y = 2.6 – 0.4x . a. Find R(x), the total revenue generated when the price of the app is x dollars. b. Find the relative extremum of R, and interpret this result. 69. Optimizing revenue. An artist sells y sculptures when the price of each sculpture is x dollars, where y = 500 - 5х. a. Find R(x), the total revenue generated when the price of each sculpture is x dollars. b. Find the relative extremum of R, and interpret this result. 70. Optimizing yield. Each apple tree yields y apples when there are x trees in an orchard, where y = 300 – 6x . a. Find R(x), the total yield generated when there are x apple trees in the orchard. b. Find the relative extremum of R, and interpret this result. Life and Physical Sciences 71. Solar eclipse. On July 2, 2019, a total solar eclipse was observable over the South Pacific Ocean and parts of South America. (Source: eclipse.gsfc.nasa.gov.) The path of the eclipse is modeled by f(t) = 0.00259t² – 0.457t + 36.237, where f(t) is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse was visible? 278
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