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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
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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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