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

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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