1: Consider a minimization problem with two extreme points x1 and x2 and two extreme directions d1 and d2. Suppose the objective function z = c x has the following values:
x1
x2
d1
d2
z = c x
Find a complete set of optimal solutions to the problem.
x = a x1 + (1 - a) x2
0 <= a <= 1
x = x2 + b d2
b >= 0
x = a x1 + (1 - a) x2 + b d2
x = a x1 + (1 - a) x2 + b1 d1 + b2 d2
b1
b2 >= 0
2: Identify a wrong entry in the simplex tableau:
x3
x4
z
3-4: Consider the minimization of
subject to the system
where all variables are non-negative. Find the missing entries A and B in the simplex tableau:
A
B
x5
A = 6
A = 4
A = 2
A = 0
B = -6
B = -2
B = 0
B = 2
5: Identify status of the simplex method from the tableau:
Your Results: