Maximize P = 2 w + x - 3 y + 3 z subject to the following conditions: 9w+x+9y+10

Question

Maximize P = 2 w + x - 3 y + 3 z subject to the following conditions: 9w+x+9y+10 z = 18, -3w - x + 3y - 4z = 0, w + x + y + 2z lessthanorequalto 14, w greaterthanorequalto 0, x greaterthanorequalto 0, y greaterthanorequalto 0, z greaterthanorequalto 0 (a) Add a non-negative slack variable to make the inequality into an equation and then enter the corresponding augmented matrix into Matlab: copy and paste it into the answer region below (only the numerical values, not the matrix name or "="). Your pasted answer should appear as a list of numbers only. (b) By using appropriate pivot operations in Matlab, find all basic solutions for this problem, it is recommended that you set it out like the worked example on page 68 of your lecture notes. In particular make sure you record the values of any feasible solutions as you will need these to answer further questions below. You should find that there is a choice of three columns that cannot contain pivots at the same time. Enter these below, for example, if columns 1,3 and 5 cannot, you would enter 1,3,5

Explanation / Answer

Tableau #1
x y z w s1 s2 s3 s4 s5 p   
1 9 10 9 1 0 0 0 0 0 18   
-1 3 -4 -3 0 1 0 0 0 0 0
1 1 2 1 0 0 1 0 0 0 14   
1 9 10 9 0 0 0 -1 0 0 18   
-1 3 -4 -3 0 0 0 0 -1 0 0
-1 3 -3 -2 0 0 0 0 0 1 0

Tableau #2
x y z w s1 s2 s3 s4 s5 p   
0 0 0 0 1 0 0 1 0 0 0
-0.6 6.6 0 0.6 0 1 0 -0.4 0 0 7.2
0.8 -0.8 0 -0.8 0 0 1 0.2 0 0 10.4   
0.1 0.9 1 0.9 0 0 0 -0.1 0 0 1.8
-0.6 6.6 0 0.6 0 0 0 -0.4 -1 0 7.2
-0.7 5.7 0 0.7 0 0 0 -0.3 0 1 5.4

Tableau #3
x y z w s1 s2 s3 s4 s5 p   
0 0 0 0 1 0 0 1 0 0 0
0 0 0 0 0 1 0 0 1 0 0
0.727273 0 0 -0.727273 0 0 1 0.151515 -0.121212 0 11.2727
0.181818 0 1 0.818182 0 0 0 -0.0454545 0.136364 0 0.818182   
-0.090909 1 0 0.0909091 0 0 0 -0.0606061 -0.151515 0 1.09091
-0.181818 0 0 0.181818 0 0 0 0.0454545 0.863636 1 -0.818182

Tableau #4
x y z w s1 s2 s3 s4 s5 p   
0 0 0 0 1 0 0 1 0 0 0
0 0 0 0 0 1 0 0 1 0 0
0 0 -4 -4 0 0 1 0.333333 -0.666667 0 8
1 0 5.5 4.5 0 0 0 -0.25 0.75 0 4.5
0 1 0.5 0.5 0 0 0 -0.08333 -0.083333 0 1.5
0 0 1 1 0 0 0 0 1 1 0

Optimal Solution: p = 0; x = 4.5, y = 1.5, z = 0, w = 0

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---