Finite Mathematics
7th Edition
ISBN: 9781337280426
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Chapter 5.2, Problem 5E
Exercises 1-24, solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. [HINT: See Example 1.]
Maximize
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4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
1
If ye y = sin x, find dy/dx and dy/dx²
at (0, 0).
Chapter 5 Solutions
Finite Mathematics
Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6ECh. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9ECh. 5.1 - In Exercises 1-26, sketch the region that...
Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 14ECh. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 27ECh. 5.1 - In Exercises 27-32, we suggest that you use...Ch. 5.1 - Prob. 29ECh. 5.1 - In Exercises 27-32, we suggest that you use...Ch. 5.1 - Prob. 31ECh. 5.1 - In Exercises 27-32, we suggest that you use...Ch. 5.1 - Resource Allocation You manage an ice cream...Ch. 5.1 - Resource Allocation Podunk Institute of Technologs...Ch. 5.1 - Nutrition, Ruff, Inc. makes dog food out of...Ch. 5.1 - Purchasing Enormous State Universitys Business...Ch. 5.1 - Nutrition Gerber Products Gerber Mixed Cereal for...Ch. 5.1 - Prob. 38ECh. 5.1 - Municipal Bond Funds The Pioneer Investment...Ch. 5.1 - Mutual Funds In 2015, the Phoenix/Zweig Advisors...Ch. 5.1 - Investments: Financial Stocks (Compare Exercise 51...Ch. 5.1 - Revenue The following spreadsheet gives annual...Ch. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - In Exercises 51-54, you are mixing x grams of...Ch. 5.1 - In Exercises 51-54, you are mixing x grams of...Ch. 5.1 - In Exercises 51-54, you are mixing x grams of...Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Prob. 17ECh. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Exercises 1-24, solve the given LP problem. If no...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Resource Allocation You manage an ice cream...Ch. 5.2 - Resource Allocation Podunk Institute of...Ch. 5.2 - Nutrition Ruff, Inc. makes dog food out of chicken...Ch. 5.2 - Purchasing Enormous State Universitys Business...Ch. 5.2 - Nutrition Gerber Products Gerber Mixed Cereal for...Ch. 5.2 - Nutrition Gerber Products Gerber Mixed Cereal for...Ch. 5.2 - Energy Efficiency You are thinking of making your...Ch. 5.2 - Energy Efficiency (Compare with Exercise 31). You...Ch. 5.2 - Prob. 33ECh. 5.2 - Bodybuilding Supplements Exercises 33-36 are based...Ch. 5.2 - Bodybuilding Supplements Exercises 33-36 are based...Ch. 5.2 - Bodybuilding Supplements Exercises 33-36 are based...Ch. 5.2 - Resource Allocation Your salami manufacturing...Ch. 5.2 - Project Design The Megabuck Hospital Corporation...Ch. 5.2 - Prob. 39ECh. 5.2 - Television Advertising On Monday evenings in April...Ch. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Investments: Financial Stocks (Compare Exercise 41...Ch. 5.2 - Investments: High-Dividend Stocks (Compare...Ch. 5.2 - Planning My friends: I, the mighty Brutus, have...Ch. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Management21 You are the service manager for a...Ch. 5.2 - If a linear programming problem has a bounded,...Ch. 5.2 - If a linear programming problem has an unbounded,...Ch. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - You are setting up an LP problem for Fly-by-Night...Ch. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.3 - Maximize p=2x+y Subject to x+2y6 x+y4 x+y4 x0,y0....Ch. 5.3 - Maximize p=x Subject to xy4 x+3y4 x0,y0. [HINT:...Ch. 5.3 - Maximize p=xy Subject to 5x5y20 2x10y40 x0,y0.Ch. 5.3 - Maximize p=2x+3y Subject to 3x+8y24 6x+4y30 x0,y0.Ch. 5.3 - Maximize p=5x4y+3z Subject to 5x+5z100 5y5z50...Ch. 5.3 - Maximize p=6x+y+3z Subject to 3x+y15 2x+2y+2z20...Ch. 5.3 - Prob. 7ECh. 5.3 - Maximize p=3x+4y+2z Subject to 3x+y+z5 x+2y+z5...Ch. 5.3 - Prob. 9ECh. 5.3 - Maximize z=3x1+4x2+6x3 Subject to 5x1x2+x31,500...Ch. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Maximize p=x+2y+z+2w+v Subject to x+y1 y+z2 z+w3...Ch. 5.3 - In Exercises 15-20 we suggest the use of...Ch. 5.3 - In Exercises 15-20 we suggest the use of...Ch. 5.3 - Prob. 17ECh. 5.3 - In Exercises 15-20 we suggest the use of...Ch. 5.3 - Prob. 19ECh. 5.3 - In Exercises 15-20 we suggest the use of...Ch. 5.3 - Purchasing You are in charge of purchases at the...Ch. 5.3 - Prob. 22ECh. 5.3 - Resource Allocation Arctic Juice Company makes...Ch. 5.3 - Purchasing Trans Global Tractor Trailers has...Ch. 5.3 - Resource Allocation The Enormous State University...Ch. 5.3 - Prob. 26ECh. 5.3 - Agriculture Your small farm encompasses 100 acres,...Ch. 5.3 - Agriculture Your farm encompasses 500 acre, and...Ch. 5.3 - Prob. 29ECh. 5.3 - Resource Allocation Repeat Exercise 29, but this...Ch. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Recycling Safety-Kleen operates the worlds largest...Ch. 5.3 - Recycling Repeat Exercise 33, but this time assume...Ch. 5.3 - Bodybuilding Supplements Exercises 35 and 36 are...Ch. 5.3 - Prob. 36ECh. 5.3 - Investing Exercises 37 and 38 are based on the...Ch. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Investments You have $100,000 that you are...Ch. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Transportation Scheduling Your publishing company...Ch. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - Are there any types of linear programming problems...Ch. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - What is a basic solution? How might one find a...Ch. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.4 - Maximize p=x+y subject to x+2y6 x+y4 2x+y8 x0,y0...Ch. 5.4 - Maximize p=3x+2y subject to x+3y6 x+y4 2x+y8 x0,y0...Ch. 5.4 - Prob. 3ECh. 5.4 - Maximize p=x+2y subject to x+y25 y10 2xy0 x0,y0.Ch. 5.4 - Maximize p=2x+5y+3z subject to x+y+z150 x+y+z100...Ch. 5.4 - Maximize p=3x+2y+2z subject to x+y+2z38 2x+y+z24...Ch. 5.4 - Maximize p=10x+20y+15z subject to x+2y+z40 2yz10...Ch. 5.4 - Maximize p=10x+10y+15z subject to xy+z12 2x2y+z15...Ch. 5.4 - Prob. 9ECh. 5.4 - Maximize p=x+y+4z+2w subject to x+y+z+w50 2x+yzw10...Ch. 5.4 - Minimize c=6x+6y subject to x+2y20 2x+y20 x0,y0.Ch. 5.4 - Minimize c=3x+2y subject to x+2y20 2x+y10 x0,y0Ch. 5.4 - Prob. 13ECh. 5.4 - Minimize c=2x+2y+3z subject to x+z100 2x+y50 y+z50...Ch. 5.4 - Minimize c=50x+50y+11z subject to 2x+z3 2x+yz2...Ch. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - In Exercises 19-24, we suggest the use of...Ch. 5.4 - Prob. 21ECh. 5.4 - In Exercises 19-24, we suggest the use of...Ch. 5.4 - In Exercises 19-24, we suggest the use of...Ch. 5.4 - Prob. 24ECh. 5.4 - Agriculture (Compare Exercise 27 in Section 6.3.)...Ch. 5.4 - Agriculture (Compare Exercise 28 in Section 6.3.)...Ch. 5.4 - Politics The political pollster Canter preparing...Ch. 5.4 - Prob. 28ECh. 5.4 - Resource Allocation Succulent Citrus produce...Ch. 5.4 - Resource Allocation Fancy Pineapple produces...Ch. 5.4 - Latin Music Sales (Digital) You are about to go...Ch. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Gaming Exercises 33-36 are based on the following...Ch. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Purchasing Federal Rent-a-Car is pulling together...Ch. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Transportation Scheduling We return 10 your...Ch. 5.4 - Prob. 46ECh. 5.4 - Finance Senator Porkbarrel habitually overdraws...Ch. 5.4 - Prob. 48ECh. 5.4 - Transportation Scheduling Your publishing company...Ch. 5.4 - Transportation Scheduling Repeat Exercise 49, but...Ch. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.5 - In Exercises 1-8, write down (without solving) the...Ch. 5.5 - In Exercises 1-8, write down (without solving) the...Ch. 5.5 - In Exercises 1-8, write down (without solving) the...Ch. 5.5 - Prob. 4ECh. 5.5 - In Exercises 1-8, write down (without solving) the...Ch. 5.5 - Prob. 6ECh. 5.5 - In Exercises 1-8, write down (without solving) the...Ch. 5.5 - Prob. 8ECh. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - Prob. 11ECh. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - Prob. 13ECh. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - In Exercises 9-22, solve the given standard...Ch. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - In Exercises 23-28, solve the game with the given...Ch. 5.5 - In Exercises 23-28, solve the game with the given...Ch. 5.5 - Prob. 26ECh. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Prob. 31ECh. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Prob. 33ECh. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Many of Exercises 29-40 are similar or identical...Ch. 5.5 - Prob. 41ECh. 5.5 - Game Theory: Marketing Your companys new portable...Ch. 5.5 - Game Theory: Morra Games A three-finger Morra game...Ch. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5 - In Exercises 1-4, sketch the region corresponding...Ch. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - In Exercises 5-8, solve the given linear...Ch. 5 - In Exercises 5-8, solve the given linear...Ch. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - In Exercises 9-18, solve the given linear...Ch. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - In Exercises 9-18, solve the given linear...Ch. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - In Exercises 31-34, you are the buyer for...Ch. 5 - In Exercises 31-34, you are the buyer for...Ch. 5 - In Exercises 31-34, you are the buyer for...Ch. 5 - Prob. 34RECh. 5 - Investments Marjory Duffins portfolio manager has...Ch. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Profit Duffin House, which is now the largest...Ch. 5 - Prob. 39RECh. 5 - Purchases You are about to place book orders from...Ch. 5 - Degree Requirements During his lunch break, John...Ch. 5 - Prob. 42RECh. 5 - Shipping On the same day that the sales department...Ch. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Prob. 46RE
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