
Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Textbook Question
Chapter 9, Problem 60RP
Graph each equation.
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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to
determine which cities Martin-Beck should construct a plant in.
Let
y₁ = 1 if a plant is constructed in Detroit; 0 if not
y₂ = 1 if a plant is constructed in Toledo; 0 if not
y₂ = 1 if a plant is constructed in Denver; 0 if not
y = 1 if a plant is constructed in Kansas City; 0 if not.
The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem.
*,, = the units shipped in thousands from plant i to distribution center j
i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and…
Consider the following mixed-integer linear program.
Max
3x1
+
4x2
s.t.
4x1
+
7x2
≤
28
8x1
+
5x2
≤
40
x1, x2 ≥ and x1 integer
(a)
Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several horizontal lines are on the graph.
The series of line segments connect the approximate points (0, 4), (3.889, 1.778), and (5, 0).
The region is above the horizontal axis, to the right of the vertical axis, and below the line segments.
At each integer value between 0 and 4 on the vertical axis, a horizontal line extends out from the vertical axis to the series of connect line segments.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several…
Consider the nonlinear optimization model stated below.
Min
s.t.
2x²-18x + 2XY + y² - 14Y + 53
x + 4Y ≤ 8
(a) Find the minimum solution to this problem.
|at (X, Y) =
(b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change?
Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by
(c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate?
If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is|
, so the actual change is a decrease of
rather than what we expected in part (b).
Chapter 9 Solutions
Prealgebra (6th Edition)
Ch. 9.1 - Coffee Consumption Use the pictograph to answer...Ch. 9.1 - Coffee Consumption Use the pictograph to answer...Ch. 9.1 - Coffee Consumption Use the pictograph to answer...Ch. 9.1 - Coffee Consumption Use the pictograph to answer...Ch. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Population Density Use this pictograph to answer...Ch. 9.1 - Prob. 8ECh. 9.1 - Population Density Use this pictograph to answer...Ch. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Household Expenses The average household expenses...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Emergency Room Visits In the United States...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Monthly Precipitation The comparison line graph...Ch. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Fat and Carbohydrates Use the table to make a...Ch. 9.1 - Life Insurance Use the information in the table to...Ch. 9.1 - Life Insurance Use the information in the table to...Ch. 9.1 - Mobile Device Accessories Use the information in...Ch. 9.1 - Mobile Device Accessories Use the information in...Ch. 9.1 - Sport Event Tickets Use the circle graph for...Ch. 9.1 - Perform the operation indicated. [6.1.4]...Ch. 9.1 - Prob. 53ECh. 9.1 - Perform the operation indicated. [6.4.2] Factor....Ch. 9.1 - Use the information in the table for exercises...Ch. 9.1 - Refer to the circle graph in exercise 51 to answer...Ch. 9.1 - Use the information in the table to construct a...Ch. 9.1 - Concept Check The college administration is...Ch. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Sales Record The double-bar graph shows the number...Ch. 9.2 - Baseball The captain of the college baseball team...Ch. 9.2 - Bowling The captain of the college bowling team...Ch. 9.2 - Prob. 15ECh. 9.2 - Gasoline Mileage Cindy and Andrea traveled to...Ch. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Cell Phone Usage The numbers of cell phone minutes...Ch. 9.2 - Swimmers' Ages The ages of 10 people swimming laps...Ch. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Find the median value. Actors in a Play The...Ch. 9.2 - Find the median value. Football Injuries The...Ch. 9.2 - Prob. 33ECh. 9.2 - Find the mode. 86, 84, 86, 87, 84, 83, 90Ch. 9.2 - Prob. 35ECh. 9.2 - Find the mode. 144, 143, 140, 141, 149, 144, 141,...Ch. 9.2 - Prob. 37ECh. 9.2 - TVs Sold The last six flat-screen television sets...Ch. 9.2 - Find the mean, median, and mode for each set of...Ch. 9.2 - Prob. 40ECh. 9.2 - Find the mean, median, and mode for each set of...Ch. 9.2 - Find the mean, median, and mode for each set of...Ch. 9.2 - Study Time Dawn studies and completes homework for...Ch. 9.2 - Restaurant Ratings Sara's Seafood Place received...Ch. 9.2 - Use the table for exercises 45 and 46. Round to...Ch. 9.2 - Use the table for exercises 45 and 46. Round to...Ch. 9.2 - Monthly Salaries A local travel office has 10...Ch. 9.2 - Track Meet A college track star ran the 100-meter...Ch. 9.2 - Prob. 49ECh. 9.2 - Find the median value. 15.276; 21.375; 18.90;...Ch. 9.2 - Evaluate. [2.6.2] x2+4forx=26Ch. 9.2 - Evaluate. [2.6.2] 35x-9forx=7Ch. 9.2 - Evaluate. [2.6.2] 2x+1forx=5Ch. 9.2 - Evaluate. [2.6.2] 3x7forx=0Ch. 9.2 - [5.1.3]Roofing Cost Wesley is putting a new roof...Ch. 9.2 - [2.3.3]Mountain Altitude The highest mountain in...Ch. 9.2 - Find the average or mean quiz score for Jake if he...Ch. 9.2 - Find the median of each of the following. a. 17,...Ch. 9.2 - Find the mode of each of the following. a. Sara...Ch. 9.3 - Describe in words the directions you move on the...Ch. 9.3 - Describe in words the directions you move on the...Ch. 9.3 - Online Orders Use the line graph to answer...Ch. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 9ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 11ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 13ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 15ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 18ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Prob. 21ECh. 9.3 - Plot and label the ordered pairs on the...Ch. 9.3 - Give the coordinates of each point. KCh. 9.3 - Prob. 24ECh. 9.3 - Give the coordinates of each point. MCh. 9.3 - Prob. 26ECh. 9.3 - Give the coordinates of each point. OCh. 9.3 - Give the coordinates of each point. PCh. 9.3 - Give the coordinates of each point. QCh. 9.3 - Prob. 30ECh. 9.3 - Give the coordinates of each point. SCh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Give the coordinates of each point. VCh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Plot and label the ordered pairs on a rectangular...Ch. 9.3 - Prob. 2QQCh. 9.3 - Plot the points corresponding to each set of...Ch. 9.3 - Concept Check Line M passes through the points...Ch. 9.4 - Prob. 1ECh. 9.4 - Is (1,3) a solution to 2x+y=5? Why or why not?Ch. 9.4 - List four ordered pairs that are solutions to the...Ch. 9.4 - List four ordered pairs that are solutions to the...Ch. 9.4 - List four ordered pairs that are solutions to the...Ch. 9.4 - List four ordered pairs that are solutions to the...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Prob. 14ECh. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Use a chart to organize your work for exercises...Ch. 9.4 - Prob. 23ECh. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Prob. 30ECh. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Prob. 32ECh. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Plot three ordered-pair solutions of the given...Ch. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 1QQCh. 9.4 - Prob. 2QQCh. 9.4 - Prob. 3QQCh. 9.4 - Prob. 4QQCh. 9 - Course Enrollment Use this pictograph to answer...Ch. 9 - Course Enrollment Use this pictograph to answer...Ch. 9 - Prob. 3RPCh. 9 - Course Enrollment Use this pictograph to answer...Ch. 9 - Prob. 5RPCh. 9 - Prob. 6RPCh. 9 - Household Budget Nancy and Wally Worzowski's...Ch. 9 - Prob. 8RPCh. 9 - Prob. 9RPCh. 9 - Household Budget Nancy and Wally Worzowski's...Ch. 9 - Prob. 11RPCh. 9 - Household Budget Nancy and Wally Worzowski's...Ch. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Prob. 16RPCh. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Population Growth The double-bar graph illustrates...Ch. 9 - Prob. 20RPCh. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Trade-in Values vs Private Sale The comparison...Ch. 9 - Circus Souvenir Use the information in the table...Ch. 9 - Prob. 30RPCh. 9 - Prob. 31RPCh. 9 - Bus Rides Use the information in the table to...Ch. 9 - Prob. 33RPCh. 9 - Find the median value. Student Enrollment The...Ch. 9 - Prob. 35RPCh. 9 - Find the median value. Pizza Delivery The numbers...Ch. 9 - Find the mean (average). Temperature Readings The...Ch. 9 - Find the mean (average). Groceries Purchased The...Ch. 9 - Find the mean (average). Textbooks Purchased The...Ch. 9 - Prob. 40RPCh. 9 - Find the mode. 22, 13, 18, 14, 13, 19Ch. 9 - Find the mode. 18, 14, 28, 18, 29, 18, 14Ch. 9 - Prob. 43RPCh. 9 - Prob. 44RPCh. 9 - Plot and label each point on the rectangular...Ch. 9 - Plot and label each point on the rectangular...Ch. 9 - Plot and label each point on the rectangular...Ch. 9 - Plot and label each point on the rectangular...Ch. 9 - Give the coordinates of each point. RCh. 9 - Give the coordinates of each point. SCh. 9 - Give the coordinates of each point. TCh. 9 - Give the coordinates of each point. UCh. 9 - Plot the points corresponding to the ordered pairs...Ch. 9 - Prob. 54RPCh. 9 - Prob. 55RPCh. 9 - List three ordered pairs that are solutions to the...Ch. 9 - Typing Speed The secretary for the JM law offices...Ch. 9 - Prob. 58RPCh. 9 - Fill in the ordered pairs so that they are...Ch. 9 - Graph each equation. y=3x1Ch. 9 - Graph each equation. y=5x4Ch. 9 - Graph each equation. y=4x6Ch. 9 - Graph each equation. y=1Ch. 9 - The ages of 5000 students on campus were recorded....Ch. 9 - The ages of 5000 students on campus were recorded....Ch. 9 - The ages of 5000 students on campus were recorded....Ch. 9 - Prob. 4TCh. 9 - The water in Toronto Harbor in Canada freezes...Ch. 9 - The water in Toronto Harbor in Canada freezes...Ch. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - The multiple bar graph indicates the number of...Ch. 9 - Prob. 10TCh. 9 - The multiple bar graph indicates the number of...Ch. 9 - The multiple bar graph indicates the number of...Ch. 9 - The multiple bar graph indicates the number of...Ch. 9 - Prob. 14TCh. 9 - A student received quiz grades of 89, 46, 85, 91,...Ch. 9 - Prob. 16TCh. 9 - Plot and label each ordered pair on the...Ch. 9 - Plot and label each ordered pair on the...Ch. 9 - Plot and label each ordered pair on the...Ch. 9 - Plot and label each ordered pair on the...Ch. 9 - Give the coordinates of each point. ACh. 9 - Give the coordinates of each point. BCh. 9 - Give the coordinates of each point. CCh. 9 - Prob. 24TCh. 9 - Plot the set of ordered pairs and then draw a line...Ch. 9 - Prob. 26TCh. 9 - Graph. y=4x2Ch. 9 - Graph. y=3x+1
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