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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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#69
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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