EBK MATHEMATICS FOR THE TRADES
10th Edition
ISBN: 9780100803053
Author: SAUNDERS
Publisher: YUZU
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Chapter 3.3, Problem 2AE
To determine
To write: The number
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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 3 Solutions
EBK MATHEMATICS FOR THE TRADES
Ch. 3.1 - Write in words. 0.72Ch. 3.1 - Write in words. 8.7Ch. 3.1 - Write in words. 12.36Ch. 3.1 - Prob. 4AECh. 3.1 - Write in words. 3.072Ch. 3.1 - Write in words. 14.091Ch. 3.1 - Write in words. 3.0024Ch. 3.1 - Write in words. 6.0083Ch. 3.1 - Prob. 9AECh. 3.1 - Write as a decimal number. Three and four tenths
Ch. 3.1 - Prob. 11AECh. 3.1 - Prob. 12AECh. 3.1 - Prob. 13AECh. 3.1 - Prob. 14AECh. 3.1 - Prob. 15AECh. 3.1 - Prob. 16AECh. 3.1 - Write as a decimal number. One hundred sixteen...Ch. 3.1 - Prob. 18AECh. 3.1 - Write as a decimal number. Two and three hundred...Ch. 3.1 - Write as a decimal number. Ten and two hundred...Ch. 3.1 - Add or subtract as shown. 14.21 + 6.8Ch. 3.1 - Prob. 2BECh. 3.1 - Add or subtract as shown. 2.83 + 12.19Ch. 3.1 - Add or subtract as shown. 52.37 + 98.74Ch. 3.1 - Add or subtract as shown. 0.687 + 0.93Ch. 3.1 - Prob. 6BECh. 3.1 - Add or subtract as shown. 507.18 + 321.42Ch. 3.1 - Prob. 8BECh. 3.1 - Add or subtract as shown. 45.6725 + 18.058Ch. 3.1 - Prob. 10BECh. 3.1 - Add or subtract as shown. 19 12.03Ch. 3.1 - Prob. 12BECh. 3.1 - Add or subtract as shown. 33.40 18.04Ch. 3.1 - Prob. 14BECh. 3.1 - Add or subtract as shown. 75.08 32.75Ch. 3.1 - Prob. 16BECh. 3.1 - Add or subtract as shown. 30 7.98Ch. 3.1 - Prob. 18BECh. 3.1 - Add or subtract as shown. 130 16.04Ch. 3.1 - Add or subtract as shown. 19 5.78Ch. 3.1 - Add or subtract as shown. 37 + 0.09 + 3.5 + 4.605Ch. 3.1 - Prob. 22BECh. 3.1 - Add or subtract as shown. 14.75 + 9 + 3.76Ch. 3.1 - Prob. 24BECh. 3.1 - Add or subtract as shown. 68.708 + 27.18Ch. 3.1 - Prob. 26BECh. 3.1 - Add or subtract as shown. 47.04 31.88Ch. 3.1 - Add or subtract as shown. 180.76 94.69Ch. 3.1 - Add or subtract as shown. 26.45 17.832Ch. 3.1 - Prob. 30BECh. 3.1 - Add or subtract as shown. 6.4 + 17.05 + 7.78Ch. 3.1 - Add or subtract as shown. 212.4 + 76 + 3.79Ch. 3.1 - Add or subtract as shown. 26.008 8.4Ch. 3.1 - Prob. 34BECh. 3.1 - Add or subtract as shown. 0.0046 + 0.073Ch. 3.1 - Add or subtract as shown. 0.038 + 0.00462Ch. 3.1 - Add or subtract as shown. 28.7 7.38 + 2.9Ch. 3.1 - Add or subtract as shown. 0.932 + 0.08 0.4Ch. 3.1 - Add or subtract as shown. 6.01 3.55 0.712Ch. 3.1 - Prob. 40BECh. 3.1 - Machine Trades What is the combined thickness of...Ch. 3.1 - Electrical Trades The combined weight of a spool...Ch. 3.1 - Electrical Trades The following are diameters of...Ch. 3.1 - Trades Management In estimating the cost of a job,...Ch. 3.1 - Metalworking Find A, B, and C.Ch. 3.1 - Plumbing A piece of pipe 8.4 in. long is cut from...Ch. 3.1 - Machine Trades A certain machine part is 2.345 in....Ch. 3.1 - Masonry Find the total cost of the materials for a...Ch. 3.1 - Masonry The specifications for a reinforced...Ch. 3.1 - Construction A plot plan of a building site showed...Ch. 3.1 - Automotive Trades A mechanic must estimate the...Ch. 3.1 - Automotive Trades A heated piston measures 8.586...Ch. 3.1 - Prob. 13CECh. 3.1 - Prob. 14CECh. 3.1 - Prob. 15CECh. 3.1 - Prob. 16CECh. 3.1 - Prob. 17CECh. 3.1 - Prob. 18CECh. 3.1 - Automotive Trades A technician renovating a truck...Ch. 3.1 - Prob. 20CECh. 3.1 - Automotive Trades An automotive technician is paid...Ch. 3.1 - Prob. 22CECh. 3.1 - Life Skills Balance this checkbook by finding the...Ch. 3.1 - Automotive Trades What is the actual cost of the...Ch. 3.1 - Add as shown. (a)...Ch. 3.2 - Multiply or divide as shown. 0.01 0.001Ch. 3.2 - Multiply or divide as shown. 10 2.15Ch. 3.2 - Multiply or divide as shown. 0.04 100Ch. 3.2 - Prob. 4AECh. 3.2 - Multiply or divide as shown. 0.7 1.2Ch. 3.2 - Prob. 6AECh. 3.2 - Multiply or divide as shown. 0.003 0.01Ch. 3.2 - Multiply or divide as shown. 7.25 0.301Ch. 3.2 - Prob. 9AECh. 3.2 - Prob. 10AECh. 3.2 - Multiply or divide as shown. 0.6 0.6 6.0Ch. 3.2 - Prob. 12AECh. 3.2 - Multiply or divide as shown. 3.618 0.6Ch. 3.2 - Prob. 14AECh. 3.2 - Multiply or divide as shown. 4.40 0.22Ch. 3.2 - Prob. 16AECh. 3.2 - Multiply or divide as shown. 0.0405 0.9Ch. 3.2 - Prob. 18AECh. 3.2 - Prob. 19AECh. 3.2 - Prob. 20AECh. 3.2 - Multiply or divide as shown. 4 0.01Ch. 3.2 - Multiply or divide as shown. 2.59 70Ch. 3.2 - Multiply or divide as shown. 44.22 6.7Ch. 3.2 - Multiply or divide as shown. 104.2 0.0320Ch. 3.2 - Multiply or divide as shown. 484 0.8Ch. 3.2 - Prob. 26AECh. 3.2 - Prob. 27AECh. 3.2 - Prob. 28AECh. 3.2 - Prob. 29AECh. 3.2 - Prob. 30AECh. 3.2 - Prob. 31AECh. 3.2 - Prob. 32AECh. 3.2 - Multiply or divide as shown. 0.0092 115Ch. 3.2 - Prob. 34AECh. 3.2 - Prob. 35AECh. 3.2 - Prob. 36AECh. 3.2 - Prob. 37AECh. 3.2 - Prob. 38AECh. 3.2 - Multiply or divide as shown. 0.062 27.5Ch. 3.2 - Round the following numbers as indicated. 42.875...Ch. 3.2 - Round the following numbers as indicated. 0.5728...Ch. 3.2 - Round the following numbers as indicated. 6.54...Ch. 3.2 - Round the following numbers as indicated. 117.6252...Ch. 3.2 - Round the following numbers as indicated. 79.135...Ch. 3.2 - Round the following numbers as indicated. 1462.87...Ch. 3.2 - Round the following numbers as indicated. 3.64937...Ch. 3.2 - Round the following numbers as indicated. 19.4839...Ch. 3.2 - Round the following numbers as indicated. 0.2164...Ch. 3.2 - Prob. 10BECh. 3.2 - Divide and round as indicated. Round to two...Ch. 3.2 - Prob. 2CECh. 3.2 - Divide and round as indicated. Round to two...Ch. 3.2 - Prob. 4CECh. 3.2 - Divide and round as indicated. Round to two...Ch. 3.2 - Divide and round as indicated. Round to two...Ch. 3.2 - Divide and round as indicated. Round to two...Ch. 3.2 - Prob. 8CECh. 3.2 - Prob. 9CECh. 3.2 - Prob. 10CECh. 3.2 - Prob. 11CECh. 3.2 - Prob. 12CECh. 3.2 - D. Divide and round as indicated. Round to the...Ch. 3.2 - Prob. 14CECh. 3.2 - Prob. 15CECh. 3.2 - Prob. 16CECh. 3.2 - D. Divide and round as indicated. Round to three...Ch. 3.2 - Prob. 18CECh. 3.2 - Prob. 19CECh. 3.2 - Prob. 20CECh. 3.2 - Prob. 1DECh. 3.2 - Prob. 2DECh. 3.2 - E. Find the average for each of the following sets...Ch. 3.2 - Prob. 4DECh. 3.2 - E. Find the average for each of the following sets...Ch. 3.2 - Prob. 6DECh. 3.2 - Prob. 1EECh. 3.2 - Allied Health How much total medication will a...Ch. 3.2 - Prob. 3EECh. 3.2 - Prob. 4EECh. 3.2 - Prob. 5EECh. 3.2 - Machine Trades How much does 15.7 sq ft of No. 16...Ch. 3.2 - Prob. 7EECh. 3.2 - Prob. 8EECh. 3.2 - Prob. 9EECh. 3.2 - Prob. 10EECh. 3.2 - Prob. 11EECh. 3.2 - Prob. 12EECh. 3.2 - Prob. 13EECh. 3.2 - Prob. 14EECh. 3.2 - Prob. 15EECh. 3.2 - Prob. 16EECh. 3.2 - Prob. 17EECh. 3.2 - Office Services The Happy Hacker electronics...Ch. 3.2 - Prob. 19EECh. 3.2 - Prob. 20EECh. 3.2 - Prob. 21EECh. 3.2 - Prob. 22EECh. 3.2 - Prob. 23EECh. 3.2 - Prob. 24EECh. 3.2 - Prob. 25EECh. 3.2 - Prob. 26EECh. 3.2 - Prob. 27EECh. 3.2 - Prob. 28EECh. 3.2 - Prob. 29EECh. 3.2 - Prob. 30EECh. 3.2 - Prob. 31EECh. 3.2 - Prob. 32EECh. 3.2 - Construction The Passive House Standard is a...Ch. 3.2 - Prob. 34EECh. 3.2 - Prob. 35EECh. 3.2 - Prob. 36EECh. 3.2 - Prob. 37EECh. 3.2 - HVAC A homeowner in the Northeast recently spent...Ch. 3.2 - Prob. 39EECh. 3.2 - Prob. 40EECh. 3.2 - Prob. 41EECh. 3.2 - Prob. 42EECh. 3.2 - Prob. 43EECh. 3.2 - Prob. 1FECh. 3.2 - Prob. 2FECh. 3.2 - Prob. 3FECh. 3.2 - Prob. 4FECh. 3.2 - Prob. 5FECh. 3.2 - Prob. 6FECh. 3.2 - Prob. 7FECh. 3.2 - Prob. 8FECh. 3.2 - Prob. 9FECh. 3.2 - Prob. 10FECh. 3.2 - Prob. 11FECh. 3.2 - Prob. 12FECh. 3.2 - Prob. 13FECh. 3.2 - Prob. 14FECh. 3.2 - Prob. 15FECh. 3.2 - Prob. 16FECh. 3.2 - Prob. 17FECh. 3.2 - Prob. 18FECh. 3.2 - Prob. 19FECh. 3.2 - Prob. 20FECh. 3.2 - Prob. 21FECh. 3.2 - Prob. 22FECh. 3.3 - Prob. 1AECh. 3.3 - Prob. 2AECh. 3.3 - Prob. 3AECh. 3.3 - Prob. 4AECh. 3.3 - Prob. 5AECh. 3.3 - Prob. 6AECh. 3.3 - Prob. 7AECh. 3.3 - Prob. 8AECh. 3.3 - Prob. 9AECh. 3.3 - Prob. 10AECh. 3.3 - Prob. 11AECh. 3.3 - Prob. 12AECh. 3.3 - Prob. 13AECh. 3.3 - Prob. 14AECh. 3.3 - Prob. 15AECh. 3.3 - Prob. 16AECh. 3.3 - Prob. 17AECh. 3.3 - Prob. 18AECh. 3.3 - Prob. 19AECh. 3.3 - Prob. 20AECh. 3.3 - Prob. 21AECh. 3.3 - Prob. 22AECh. 3.3 - Prob. 23AECh. 3.3 - Prob. 24AECh. 3.3 - Prob. 25AECh. 3.3 - Prob. 26AECh. 3.3 - Prob. 27AECh. 3.3 - Prob. 28AECh. 3.3 - Prob. 1BECh. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Prob. 4BECh. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Prob. 8BECh. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Prob. 10BECh. 3.3 - Calculate in decimal form. Round to agree with the...Ch. 3.3 - Prob. 12BECh. 3.3 - Allied Health If one tablet of calcium...Ch. 3.3 - Flooring and Carpeting Estimates of matched or...Ch. 3.3 - Roofing If a roofer lays 1012 squares of shingles...Ch. 3.3 - Machine Trades A bearing journal measures 1.996...Ch. 3.3 - Interior Design Complete the following invoice for...Ch. 3.3 - Construction A land developer purchased a piece of...Ch. 3.3 - Machine Trades Find the corner measurement A...Ch. 3.3 - Automotive Trades A cylinder is normally 3716 in....Ch. 3.3 - Plumbers deal with measurements in inches and...Ch. 3.3 - Plumbing To fit a 45 degree connection, a plumber...Ch. 3.3 - Electronics The frequency of a waveform or...Ch. 3.3 - Water/Wastewater Treatment A reservoir is used at...Ch. 3.3 - Sheet Metal Trades At one time the thickness of...Ch. 3.3 - Prob. 14CECh. 3 - (a) Write or pronounce a decimal number in words....Ch. 3 - Add, subtract, multiply, and divide decimal...Ch. 3 - Find averages. Find the average of 4.2, 4.8, 5.7,...Ch. 3 - Work with decimal fractions. (a) Write as a...Ch. 3 - Solve practical problems involving decimal...Ch. 3 - Write in words. 0.9Ch. 3 - Prob. 2APSCh. 3 - A. Write in words. 23.164Ch. 3 - A. Write in words. 63.219Ch. 3 - A. Write in words. 9.3Ch. 3 - A. Write in words. 3.45Ch. 3 - Prob. 7APSCh. 3 - Write in words. 15.037Ch. 3 - Write as decimal numbers. Seven hundredthsCh. 3 - Write as decimal numbers. Eighteen thousandthsCh. 3 - Write as decimal numbers. Two hundred and eight...Ch. 3 - Write as decimal numbers. Sixteen and seventeen...Ch. 3 - Write as decimal numbers. Sixty-three and...Ch. 3 - Prob. 14APSCh. 3 - Write as decimal numbers. Five and sixty-three...Ch. 3 - Prob. 16APSCh. 3 - Prob. 1BPSCh. 3 - B. Add or subtract as shown. 18.8 + 156.16Ch. 3 - B. Add or subtract as shown. 7.52 + 11.77Ch. 3 - B. Add or subtract as shown. 26 + 0.06Ch. 3 - B. Add or subtract as shown. 3.68 1.74Ch. 3 - Add or subtract as shown. 12.46 8.51Ch. 3 - Prob. 7BPSCh. 3 - Prob. 8BPSCh. 3 - Prob. 9BPSCh. 3 - Add or subtract as shown. 0.232 + 5.079Ch. 3 - Prob. 11BPSCh. 3 - Prob. 12BPSCh. 3 - Prob. 13BPSCh. 3 - Prob. 14BPSCh. 3 - Prob. 15BPSCh. 3 - Prob. 16BPSCh. 3 - B. Add or subtract as shown. 315+1.08Ch. 3 - Prob. 18BPSCh. 3 - Prob. 19BPSCh. 3 - B. Add or subtract as shown. 8.1+0.47145Ch. 3 - Prob. 1CPSCh. 3 - C. Calculate as shown. 0.06 0.05Ch. 3 - Prob. 3CPSCh. 3 - Prob. 4CPSCh. 3 - Prob. 5CPSCh. 3 - C. Calculate as shown. 1.17 4.5Ch. 3 - Prob. 7CPSCh. 3 - Prob. 8CPSCh. 3 - Prob. 9CPSCh. 3 - C. Calculate as shown. 0.078 0.3Ch. 3 - Prob. 11CPSCh. 3 - Prob. 12CPSCh. 3 - Prob. 13CPSCh. 3 - Prob. 14CPSCh. 3 - 4.2+4.61.22.7321+0.41Ch. 3 - 7.23.251.33.5+5.74.02.8Ch. 3 - C. Calculate as shown. 1.2 + 0.7 2.2 + 1.6Ch. 3 - Prob. 18CPSCh. 3 - Round to two decimal digits. 0.007 0.03Ch. 3 - Prob. 20CPSCh. 3 - Round to two decimal digits. 17.8 6.4Ch. 3 - Prob. 22CPSCh. 3 - Prob. 23CPSCh. 3 - Prob. 24CPSCh. 3 - Round to three decimal places. 0.04 0.076Ch. 3 - Prob. 26CPSCh. 3 - Round to three decimal places. 17.6 0.082Ch. 3 - Prob. 28CPSCh. 3 - Round to three decimal places. 27.0072Ch. 3 - Prob. 30CPSCh. 3 - Round to the nearest tenth. 0.08 0.053Ch. 3 - Prob. 32CPSCh. 3 - Round to the nearest tenth. 18.76 4.05Ch. 3 - Round to the nearest tenth. 0.91 0.97Ch. 3 - Round to the nearest tenth. 47.233Ch. 3 - Prob. 36CPSCh. 3 - D. Write as a decimal number. 116Ch. 3 - Prob. 2DPSCh. 3 - D. Write as a decimal number. 532Ch. 3 - Prob. 4DPSCh. 3 - D. Write as a decimal number. 118Ch. 3 - Prob. 6DPSCh. 3 - Write as a decimal number. 21120Ch. 3 - Write as a decimal number. 116Ch. 3 - Prob. 9DPSCh. 3 - Prob. 10DPSCh. 3 - Write as a decimal number. 2516Ch. 3 - Prob. 12DPSCh. 3 - Prob. 13DPSCh. 3 - Prob. 14DPSCh. 3 - Write in decimal form, calculate, round to two...Ch. 3 - Prob. 16DPSCh. 3 - Prob. 17DPSCh. 3 - Machine Trades A 516-in. bolt weighs 0.43 lb. How...Ch. 3 - Metalworking Twelve equally spaced holes are to be...Ch. 3 - Plumbing A plumber finds the length of pipe needed...Ch. 3 - Prob. 4EPSCh. 3 - Prob. 5EPSCh. 3 - Prob. 6EPSCh. 3 - Prob. 7EPSCh. 3 - Prob. 8EPSCh. 3 - Prob. 9EPSCh. 3 - Prob. 10EPSCh. 3 - Prob. 11EPSCh. 3 - Trades Management When the owners of the Better...Ch. 3 - Prob. 13EPSCh. 3 - Sheet Metal Trades To determine the average...Ch. 3 - Prob. 15EPSCh. 3 - Prob. 16EPSCh. 3 - Prob. 17EPSCh. 3 - Prob. 18EPSCh. 3 - Prob. 19EPSCh. 3 - Prob. 20EPSCh. 3 - Prob. 21EPSCh. 3 - Prob. 22EPSCh. 3 - Prob. 23EPSCh. 3 - Printing A 614-page book was printed on paper...Ch. 3 - Allied Health The primary care physician has...Ch. 3 - Prob. 26EPSCh. 3 - Prob. 27EPSCh. 3 - Prob. 28EPSCh. 3 - Prob. 29EPSCh. 3 - Plumbing The inside diameter (I.D.) and outside...Ch. 3 - Prob. 31EPSCh. 3 - Office Services A shop technician earns 18.26 per...Ch. 3 - Prob. 33EPSCh. 3 - Prob. 34EPSCh. 3 - Prob. 35EPSCh. 3 - Prob. 36EPSCh. 3 - Prob. 37EPSCh. 3 - Prob. 38EPSCh. 3 - Prob. 39EPSCh. 3 - Prob. 40EPSCh. 3 - Prob. 41EPSCh. 3 - Prob. 42EPSCh. 3 - Prob. 43EPSCh. 3 - Prob. 44EPSCh. 3 - Prob. 45EPSCh. 3 - Prob. 46EPSCh. 3 - Life Skills A certain electric company charges...Ch. 3 - Plumbing A plumber replaced a showerhead that used...Ch. 3 - Life Skills During the severe droughts in...Ch. 3 - Prob. 50EPSCh. 3 - Prob. 51EPSCh. 3 - Prob. 52EPSCh. 3 - Prob. 53EPSCh. 3 - Construction Over the course of a building...
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