Maximize Z = 3X1 + 2X2 + X3

Subject to :

X1+ 2X2 +X3 ≤ 430

3X1 + 2X3 = 460

X1+ 4X2 = 420

X1 + X2,X3 ≥ 0

Mumbai University > Mechanical Engineering > Sem 7 > Production planning and control

Marks: 10 M

Year: Dec 2015

Convert Given Constraints into Balanced form

X1+ 2X2 +X3 = 430

3X1 + 2X3 ≤ 460

X1+ 4X2 ≤ 420

X1 + X2,X3 ≥ 0

And Objective function

Z = 3X1 + 2X2 + X3 + 0S1 + 0S2 + 0S3

Table 1

4 most value for positive maximization

Therefore, Leaving Variable = S2

Entering Variable = x1

Row Operations

R2’ = R2/3

R1’ = R1 - R2’

R3’ = R3 - R2’

Table 2

Table 3

Leaving Variable = S3

Entering Variable = X2

Therefore, Row Operation

R3’’ = R3’/4

R2’’ = R2’

R1’’ = R1 - 2R3’’

Therefore all the values in Cj - Zj⪬ 0

Therefore above Table gives Optimum Solution

Z = 593.33

X1 = 153.33

X2 = 162.67

X3 = 0