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MATHS - STATS PROBLEMS WITH SOLUTIONS

Question # 00011133
Subject: Mathematics
Due on: 04/05/2014
Posted On: 03/28/2014 08:50 PM

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1 write the initial tableau for the following linear programing problem.do not solve
z=10x + 6x -8x

5x-2x+6x<=20
10x+4x-6x=0


2circle the pivot element in the following tableaus and write the pivot row operations and then write the resulting tableau after the pivot only perform one pivot
A
-1/3 r1 - -> R1
-5.justanswer.com/math-homework/8d2jb-finite-math-ch-4-5-i-need-help-questions.html#">R2 + R3 - - > R3

X x x s s z
1 3 3 1 0 0 50
0 2 10 2 1 0 140
0 -3 -14 8 0 1 400

B
X x x s s s z
2 2 1 1 0 0 0 12
1 2 3 0 1 0 0 45
3 -1 1 0 0 1 0 -2
-2 -1 1 0 0 1 0 0

C
X x x s s a z
15 11 7 1 0 0 0 30
5 8 1 0 1 0 0 72
-2 6 3 0 0 1 0 30
-55 -75 2 0 0 0 1 450

10- given the following linear programing problem and final tableau state the optimal solution
Maximize z = 1.75x + 5x subject to
X + 5x <= 150
X + 2x <= 90
2x + x =
The final tableau is
X x s s s z
0 1 1/3 -1/3 0 0 20
1 0 -2/3 5/3 0 0 50
0 0 1 -3 1 0 30
0 0 1/6 19/12 0 0 335/2


11- find the initial tableau of the dual of the following linear programing problem
Minimize z = 6x + 8x +16x subject to
2x + x >= 6
X + 2x >= 8
X,x,x>= 0

12- given the following final tableau that was solved using the dual method state the optimal where it occurs

Y y x x x w
0 1 ½ -1 0 0 8
1 0 -1/2 2 0 0 4
0 0 2 -9 1 0 12
0 0 5 10 0 1 320

13- given the following linear programing problem write the initial tableau
A
Maximize z= 3x + 2x subject to
X + 3x =4
X,x >= 0


B
Minimize z=15x – 10x subject to
5x + 3x = 4
X,x>=0


14- given the following final tableau for a minimization problem that was solved by maximizing the opposite of the objective,state the minimal value and where it occurs
X x x s s s w
2 0 1 2 0 -1 0 40
10 0 0 -40 1 10 0 800
0 1 0 -1 0 1 0 60
100 0 0 100 0 100 1 -26000


15- given the following linear programing problem,write the initial tableau
Maximize z=3x + 4 x subject to
5x + 2x =0

16- this tableau is a final tableau,write the solution assuming the original problem was a standard maximization problem. pivot one time using row 2 column 2 and then compare the tableau to the one given and interpret the results.

X x s s s z
0 23/3 1 0 -2/3 0 94
0 5/3 0 1 -2/3 0 10
1 2/3 0 0 1/3 0 25
0 0 0 0 5 1 375


17- graph the feasible region for the following system of inequalities
-2 < x < 4
0 <= y 6




18- given the following corner points state the maximum value of the objective function and the ordered pair where it occurs

Maximize C= 3x – 2y
Corner points (2,2) (4,2) and (4,1)







19- use the graphical method to solve the following inear programing problem
Maximize C= 3x + 2y subject to
x-2y>=-2
x+2y>=6
0<=y<=2
0<=x<=4







20- to pour a concrete sidewalk takes 2 hrs of preparation and 3hrs of finishing. To pour a concrete patio takes 4 hrs of preparation and 3 hrs of finishing. There are 8 hrs available for preparation and 21 hrs available for finishing. ABC concrete company makes a profit of $450on a sidewalk and $700 on a patio how many sidewalks and patios should the company construct to maximize the profit? Setup a system of inequalities for this problem, identify all variables used, and give the objective function but don’t solve.


Objective

Constraints

Tags solutions problems stats maths following tableau given programing subject problem final linear write pivot initial preparation finishing concrete state dual sidewalk method objective value points function to5x solved using patio pour takes profit company

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Preview: initial xxxxxxx of xxx dual of xxx following linear xxxxxxxxxx problemMinimize x xx 8y xxx subject to2x x 6x 2y xxxxxxx 0 xxxxxxxx xxxx error xxxxx is no x in constraints xxx given xxx xxxxxxxxx final xxxxxxx that was xxxxxx using the xxxx method xxxxx xxx optimal xxxxx it occursY1 xx x1 x2 xx w0 x xx 0 x 81 0 xxxx 2 0 x 40 x x -9 x 0 120 x 5 10 x 1 xxx xxxxxxxx Optimal xxxxxxxx w 320 xxxx y1 4, xx 8 xxx xxxxx the xxxxxxxxx linear programing xxxxxxx write the xxxxxxx tableauAMaximize x xx 2y xxxxxxx to X xx 6 X x 4X,y x xxxxxxxx initial xxxxxxxxxxx be x x s1 s2 x 1 x x 0 x 6 1 x 0 -1 x 4 xx xx 0 x 1 0 xxxxxxxxx z15x 10y xxxxxxx to5x xx xxxx y x X,Y 0 xxxxxxxx Initial tableauwill xx x x xx s2 xx 5 3 x.....
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