Applied Mathematics for Business and Economics

Lecture Note Linear Programming (LP)

PH=+1.2 L

L

Subjecto to
10 12 1, 920
5 3 780
,0

HL

HL

HL

+≤

+≤

≥

• 
  
  
  
  • 
    
  
  
  
  

• •

()0, 0 (156, 0)

()0,160

(120, 60)

L

H

5 HL+ 3 = 780

10 HL+ 12 =1, 920

Corner

Point

Value of

PH=1.2 +

()156, 0^ 187.2

(120, 60)^204

()0,160^160

(0, 0)^0

From this table, we see that the largest value of the objective function over the

feasibility region occurs at the point(120, 60).

Example 2
Find the largest and the smallest values of Fx= 34 + ysubject to the following

inequalities:
315
43 2
,0

xy

xy

xy

4

+ ≤

+ ≤

≥

Corner

Point

Value of

Pxy= 34 +

(0, 0)^0

()0, 5^20

()3, 4^25

(6, 0)^18

• 
  
  
  
  • ( )
    3, 4
  
  
  
  


• •

43 24xy+=

xy+ 315 =

(0, 0)

()0, 5

(6, 0)