Question

Using the graphical method, described in class, determine the optimal
solution(s) (if they exist) for the linear program. If no optimal exists, then indicate
that and explain why no optimal solution exists.

(a)
Maximize : z = 2x1 + 8x2

Subject to :

3x1 ≤ 12
x1 + 4x2 ≤ 24
x1 ≥ 0
x2 ≥ 0

(b)
Maximize : z = 2x1 − 3x2
Subject to :

6x1 − 3x2 ≤ −9
x1 ≤ 0
x2 ≤ 0

Answer 1

a) 3x1= 12 , x1=4

x1+4x2=24 , can be drwan by joining the points (0,6) and (24,0)

x1=0 is the x2 axis and x2=0 is the x1 axis

b)

Z=2x1-3x2

The line 6x1-3x2=-9 can be drawn using the points (0,3) and (-1.5,0)

Here objective function has unbounded solution.

Hence no optimal solution exists.