Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Please do on paper...
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 1x2 + 2x3
Subject to:
2x1 + 2x2 + 1x3 >= J
5x1 + 6x2 + 7x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 15
K = 17
Please do on paper..
Question 3: Graphically solve the following
problem.
Minimize the cost = X + 2 Y
Subject
to: X+3Y >= 90
8X
+ 2Y >= 160
3X
+ 2Y >= 120
Y <= 70
X,Y >= 0
What is the optimal solution?
Change the right hand side of constraint 2 to 140 (instead of
160) and resolve the problem. What is the new optimal
solution?
Write the dual maximization problem, and then solve both the
primal and dual problems with the simplex method. (For the dual
problem, use x1, x2, and x3 as the variables and f as the
function.) Minimize g = 6y1 + 28y2 subject to 2y1 + y2 ≥ 14 y1 +
3y2 ≥ 14 y1 + 4y2 ≥ 17 . primal g = primal y1 = primal y2 = dual f
= dual x1 = dual x2 = dual x3 =
Consider the LP problem below: Minimize: ? = −2? + ? Subject
to:
3? + 4? ≤ 80 −3? + 4? ≥ 8 ? + 4? ≥ 40
a) Solve the above problem using the simplex method of
solution.
b) Comment on the nature of solution to the above problem and
hence, interpret your answer
this is a quantitative method for decidion making question. Linear
programing problems using simplex tableau method