Question

4.3. The following questions below apply to the linear program be handled? z 3x113x213x maximize subject to X1 +X2 7 x +3x2+2x3s15 2x2 3x39 XI, X2, X320 with optimal basis {x\, X2, X3 ) and 5/2 3/2 -3/2 3/2 В 1 -1 1 All of the questions are independent. ( What is the solution to the problem? What are the optimal dual variables?

Answer 1

I think It's primal to dual method. I've solved it in that way. If it is another method just comment I'll edit the answer. BUT PLEASE DO ME A FAVOR BY LIKING THIS ANSWER! Thank you!

Solution:
Primal is (Solution steps of Primal)

MAX zx = 3 x1 + 13 x2 + 13 x3

subject to

x1 + x2 ≤ 7 x1 + 3 x2 + 2 x3 ≤ 15 2 x2 + 3 x3 ≤ 9

and x1,x2,x3≥0;

Dual is (Solution steps of Dual)

MIN zy = 7 y1 + 15 y2 + 9 y3

subject to

y1 + y2 ≥ 3 y1 + 3 y2 + 2 y3 ≥ 13 2 y2 + 3 y3 ≥ 13

and y1,y2,y3≥0;