EBK SURVEY OF MATHEMATICS WITH APPLICAT
10th Edition
ISBN: 9780134112183
Author: RUNDE
Publisher: YUZU
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Chapter 1.2, Problem 40E
To determine
To estimate: The number of grapes.
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Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction
of the objective function. Use you sketch to find an optimal solution to the
program. State the optimal solution and give the objective value for this
solution.
maximize +22
subject to 1 + 2x2 ≤ 4,
1 +3x2 ≤ 12,
x1, x2 ≥0
(b) For the following linear programme, sketch the feasible region and the direction
of the objective function. Explain, making reference to your sketch, why this
linear programme is unbounded.
maximize
₁+%2
subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
x1,x20
Give any feasible solution to the linear programme for which the objective
value is 40 (you do not need to justify your answer).
find the domain of the function f(x)
Chapter 1 Solutions
EBK SURVEY OF MATHEMATICS WITH APPLICAT
Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 1-8, fill in the blank with an...Ch. 1.1 - In Exercises 9-12, use inductive reasoning to...Ch. 1.1 - In Exercises 9-12, use inductive reasoning to...
Ch. 1.1 - In Exercises 9-12, use inductive reasoning to...Ch. 1.1 - In Exercises 9-12, use inductive reasoning to...Ch. 1.1 - In Exercises 13-16, draw the next figure in the...Ch. 1.1 - In Exercises 13-16, draw the next figure in the...Ch. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - In Exercises 17-26, use inductive reasoning to...Ch. 1.1 - Find the letter that is the 118th entry in the...Ch. 1.1 - a. Select a variety of one- and two-digit numbers...Ch. 1.1 - A Square Pattern The ancient Greeks labeled...Ch. 1.1 - A Triangular Pattern The ancient Greeks labeled...Ch. 1.1 - Quilt Design The pattern shown is taken from a...Ch. 1.1 - Triangles in a Triangle Four rows of a triangular...Ch. 1.1 - Video Games The graph below shows the amount of...Ch. 1.1 - Broadway Tickets The graph below shows the average...Ch. 1.1 - In Exercises 35 and 36, draw the next diagram in...Ch. 1.1 - Prob. 36ECh. 1.1 - Pick any number, multiply the number by 3, add 6...Ch. 1.1 - Pick any number and multiply the number by 4. Add...Ch. 1.1 - Prob. 39ECh. 1.1 - Pick any number and add 10 to the number. Divide...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - In Exercises 41-46, find a counterexample to show...Ch. 1.1 - Interior Angles of a Triangle a. Construct a...Ch. 1.1 - Interior Angles of a Quadrilateral a. Construct a...Ch. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Complete the following square of numbers. Explain...Ch. 1.1 - Prob. 52ECh. 1.1 - Recreational Mathematics 53. is to as is toCh. 1.2 - In Exercises 1-2, fill in the blank with an...Ch. 1.2 - In Exercises 1-2, fill in the blank with an...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - In Exercises 3-57, your answers may vary from the...Ch. 1.2 - Monthly Expenses Lis total monthly expenses...Ch. 1.2 - Estimating Weights In a tug of war, the weight of...Ch. 1.2 - Picking Strawberries Chuck hires 11 people to pick...Ch. 1.2 - Estimating Time Donna is a long-distance runner...Ch. 1.2 - Currency Estimate the difference in the value of...Ch. 1.2 - The Cost of a Vacation The Kleins are planning a...Ch. 1.2 - The Pacific Coast Highway Below is a map of...Ch. 1.2 - The Olympic Peninsula Following is a map of the...Ch. 1.2 - Coffee Consumption The circle graph below shows...Ch. 1.2 - Exercising The circle graph below shows the...Ch. 1.2 - An Aging Population The bar graph below shows...Ch. 1.2 - Gaining Weight The graph below shows that as a...Ch. 1.2 - Land Ownership by the Federal Government The...Ch. 1.2 - Calories and Exercise The chart on page 17 shows...Ch. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - In Exercises 45 and 46, if each square represents...Ch. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 58ECh. 1.2 - A Million Dollars a. Estimate the time it would...Ch. 1.3 - Reading a Map The scale on a map is 1 inch = 12...Ch. 1.3 - Blueprints Tony, an architect, is designing a new...Ch. 1.3 - Height of a Tree At a given time of day, the ratio...Ch. 1.3 - Grass Seed A bag of Turf Builder Sun and Shade Mix...Ch. 1.3 - College Tuition According to the College Board,...Ch. 1.3 - Smartphone Price According to International Data...Ch. 1.3 - How Americans Spend Their Money The circle graph...Ch. 1.3 - Bachelors Degrees The circle graph below shows the...Ch. 1.3 - Housing Market The following table shows the five...Ch. 1.3 - Subway Cost Chandler buys a monthly MetroCard,...Ch. 1.3 - Home Theater System Jackson wants to purchase a...Ch. 1.3 - Checking Account The balance in Gabrielas checking...Ch. 1.3 - Buying a House The Browns want to purchase a house...Ch. 1.3 - Prob. 14ECh. 1.3 - Playing a Lottery In one state lottery game, you...Ch. 1.3 - Energy Value and Energy Consumption The table...Ch. 1.3 - Gas Mileage Wendy fills her gas tank completely...Ch. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Profit Margins The following chart shows retail...Ch. 1.3 - Prob. 23ECh. 1.3 - Leaking Faucet A faucet is leaking at a rate of...Ch. 1.3 - Wasted Water A faucet leaks 1 oz of water per...Ch. 1.3 - Airport Parking The chart below shows parking...Ch. 1.3 - Tire Pressure When a cars tire pressure is 30...Ch. 1.3 - Prob. 28ECh. 1.3 - Adjusting for Inflation Assume that the rate of...Ch. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Who Will Win? Steve and Mark ran a 100-yard race....Ch. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Cube If the length, width, and height of a cube...Ch. 1.3 - Pole in a Lake A pole is in the middle of a small...Ch. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Palindromes A palindrome is a number (or word)...Ch. 1.3 - Below is a photo of the keyboard of a phone...Ch. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Cuts in Cheese If you make the three complete cuts...Ch. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - In Exercises 53-55, use the three magic squares...Ch. 1.3 - In Exercises 53-55, use the three magic squares...Ch. 1.3 - In Exercises 53-55, use the three magic squares...Ch. 1.3 - Prob. 56ECh. 1.3 - Prob. 57ECh. 1.3 - Prob. 58ECh. 1.3 - Consecutive Digits Place the digits 1 through 8 in...Ch. 1.3 - A Digital Clock Digital clocks display numerals by...Ch. 1.3 - Prob. 61ECh. 1.3 - Prob. 62ECh. 1.3 - Prob. 63ECh. 1.3 - Prob. 64ECh. 1.3 - Finding the Area Rectangle ABCD is made up...Ch. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1 - In Exercises 1-8, use inductive reasoning to...Ch. 1 - In Exercises 1-8 use inductive reasoning to...Ch. 1 - In Exercises 1-8, use inductive reasoning to...Ch. 1 - In Exercises 1-8, use inductive reasoning to...Ch. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - In Exercises 1-8, use inductive reasoning to...Ch. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Pick any number and multiply the number by 10. Add...Ch. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - In Exercises 13-25, estimate the answer. Your...Ch. 1 - In Exercises 13-25, estimate the answer. Your...Ch. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Sales Tax Estimate the sales tax on a boat that...Ch. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - A Walking Path The scale of the map is 14in. = 0.1...Ch. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Applying Fertilizer Ronaldo needs to apply...Ch. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Crossing Time Zones The international date line is...Ch. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Magic Square Create a magic square by using the...Ch. 1 - Prob. 40RECh. 1 - Brothers and Sisters Jim has four more brothers...Ch. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - The Sum of Numbers Find the sum of the first 500...Ch. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Sum of Numbers Place the numbers 1 through 12 in...Ch. 1 - Prob. 53RECh. 1 - Prob. 1TCh. 1 - Prob. 2TCh. 1 - Prob. 3TCh. 1 - Prob. 4TCh. 1 - Prob. 5TCh. 1 - Estimating Area If each square represents one...Ch. 1 - Body Mass Index The federal government gives a...Ch. 1 - Prob. 8TCh. 1 - Prob. 9TCh. 1 - Prob. 10TCh. 1 - Prob. 11TCh. 1 - Prob. 12TCh. 1 - Prob. 13TCh. 1 - Prob. 14TCh. 1 - Prob. 15TCh. 1 - Prob. 16TCh. 1 - Prob. 17TCh. 1 - Prob. 18TCh. 1 - Prob. 19TCh. 1 - Prob. 20T
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