Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 58, Problem 29AR
To determine
The lengths OA, OB and OC.
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b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau, and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize ₁ - 2x2+x34x4
subject to 2x1+x22x3x41,
5x1 + x2-x3-×4 ≤ −1,
2x1+x2-x3-34
2,
1, 2, 3, 40.
Suppose we have a linear program in standard equation form
maximize cTx
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) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1
x2 x3
81 82
83
84
81
-2 0
1 1 0
0
0
3
82
3 0
-2 0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0 -1
1
4
-2 -2 0
11
0
0-4
0
-8
Chapter 58 Solutions
Mathematics For Machine Technology
Ch. 58 - Add, subtract, multiply, or divide each of the...Ch. 58 - Determine A.Ch. 58 - Prob. 3ARCh. 58 - Express 68.85 as degrees and minutes.Ch. 58 - Express 64.1420 as degrees, minutes, and seconds.Ch. 58 - Express 3723' as decimal degrees to 2 decimal...Ch. 58 - Express 10338'43" as decimal degrees to 4 decimal...Ch. 58 - Using a simple protractor, measure each of the...Ch. 58 - Prob. 9ARCh. 58 - Write the complement of each of the following...
Ch. 58 - Write the complement of each of the following...Ch. 58 - Given: ABCD and FEGH . Determine the value of each...Ch. 58 - a. Determine: (1) 1 (2) Side a b. Determine: (1) 1...Ch. 58 - a. Given: a=8.400 and b=9.200 . Find c. b. Given:...Ch. 58 - Compute 1.Ch. 58 - Determine the circumference of a circle that has a...Ch. 58 - Determine the diameter of a circle that has a...Ch. 58 - a. Given: CD=184 mm and CE=118 mm. Determine CF...Ch. 58 - a. Given: EB=5.150. Determine AE . b. Given:...Ch. 58 - Given: Points A and E are tangent points. EB is a...Ch. 58 - a. Given: AC=110andr=4.700 Compute arc length AC...Ch. 58 - a. Given: Dia H=14.520 and d=8.300. Compute Dia M....Ch. 58 - Prob. 23ARCh. 58 - a. Given: x=360 inches and y=5.10 inches. Compute...Ch. 58 - Prob. 25ARCh. 58 - A flat is cut on a circular piece as shown....Ch. 58 - A spur gear is shown. Pitch circles of spur gears...Ch. 58 - Determine the arc length from point C to point D...Ch. 58 - Prob. 29ARCh. 58 - Determine dimension x to 3 decimal places.Ch. 58 - Refer to the drill jig shown. Determine 1.Ch. 58 - Prob. 32ARCh. 58 - Prob. 33ARCh. 58 - Lay out the template shown. Make the layout full...
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